View source for Math 302: Mathematics for Engineering 1

== Catalog Information ==

=== Title ===
Mathematics for Engineering 1.

=== (Credit Hours:Lecture Hours:Lab Hours) ===
(4:4:0)

=== Offered ===
F, W

=== Prerequisite ===
[[Math 113]] and passing grade on required preparatory exam taken during first week of class. (Practice exams available on class website.)

=== Description ===
Multivariable calculus, linear algebra, and numerical methods.

== Desired Learning Outcomes ==
This course is designed to give students from the College of Engineering and Technology the mathematics background necessary to succeed in their chosen field.

=== Prerequisites ===

Students are expected to have completed [[Math 113]].

=== Minimal learning outcomes ===

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# Rectangular Space Coordinates; Vectors in Three-Dimensional Space
#* Define the following:
#** Cartesian coordinates of a point
#** sphere
#** symmetry about a point, a line, and a plane
#** vector
#** components of a vector
#** vector addition
#** scalar multiplication
#** zero vector
#** vector subtraction
#** vector norm (magnitude, length)
#** unit vector
#** coordinate unit vectors i, j, k
#** linear combination of unit vectors
#* Plot points in three-dimensional space.
#* Calculate the distance between two points in two-dimensional space and 3-dimensional space
#* Write the equation of a sphere centered about a given point with a given radius. Determine the center and radius of a sphere, given its equation.
#* Write the component equations of a line that passes through two given points.
#* Write the component equations of a line segment with given endpoints.
#* Find the midpoint of a given line segment.
#* Find the points of symmetry about a point, line, or plane.
#* Represent a vector by each of the following:
#** components
#** a linear combination of coordinate unit vectors
#* Carry out the vector operations:
#** addition
#** scalar multiplication
#** subtraction
#* Represent the operations of vector addition, scalar multiplication and norm geometrically.
#* Find the norm (magnitude, length) of a vector. Determine whether two vectors are parallel.
#* Recall, apply and verify the basic properties of vector addition, scalar multiplication and norm.
#* Model and solve application problems using vectors.
# The Dot Product
#* Define the following:
#** dot product.
#** perpendicular vectors.
#** unit vector in the direction of a vector a, denoted u_a.
#** the projection of a on b, denoted proj_b a.
#** the b-component of a, denoted comp_b a.
#** the direction cosines of a vector.
#** the direction angles of a vector.
#** the Schwarz Inequality.
#** the work done by a constant force on an object.
#** the dot product test for perpendicular vectors.
#** the dot product test for parallel vectors.
#** geometric interpretation of the dot product
#* Evaluate a dot product from the coordinate formula or the angle formula.
#* Interpret the dot product geometrically.
#* Evaluate the following using the dot product:
#** the length of a vector.
#** the angle between two vectors.
#** u_a, the unit vector in the direction of a vector a.
#** proj_b a, the projection of a on b.
#** comp_b a, the b-component of a.
#** the direction cosines of a vector.
#** the direction angles of a vector.
#** the work done by a constant force on an object.
#* Prove and verify the Schwarz Inequality.
#* Prove and apply the dot product tests for perpendicular and parallel vectors.
#* Recall and apply the properties of the dot product.
#* Prove identities involving the dot product.
#* Solve application problems involving the dot product.
#* Extend the vector operations and related identities for addition, scalar multiplication, and dot product to higher dimensions.
# The Cross Product
#* Define the following:
#** the cross product of two vectors
#** scalar triple product
#* Evaluate a cross product from the the coordinate formula or angle formula.
#* Interpret the cross product geometrically.
#* Evaluate the following using the cross product:
#** a vector perpendicular to two given vectors.
#** the area of a parallelogram.
#** the area or a triangle.
#** moment of force or moment of torque.
#* Evaluate scalar triple products.
#* Use the scalar triple product to determine the following:
#** volume of a parallelepiped.
#** whether or not three vectors are coplanar.
#* Recall and apply the properties of the cross product and scalar triple product.
#* Prove identities involving the cross product and the scalar triple product.
#* Solve application problems involving the cross product and scalar triple product.
# Lines
#*Define the following:
#** direction vector for a line
#** vector equation of a line
#** scalar parametric equations of a line
#** Cartesian equations or symmetric form of a line
#* Represent a line in 3-space by:
#** a vector equation
#** scalar parametric equations
#** Cartesian equations
#* Find the equation(s) representing a line given information about
#** a point of the line and the direction of the line or
#** two points contained in the line.
#** a point and a parallel line.
#** a point and perpendicular to a plane.
#** two planes intersecting in the line.
#* Find the distance from a point to a line.
#* Solve application problems involving lines.
# Planes
#* Define the following:
#** normal vector to a plane
#** cartesian equation of a plane
#** parametric equation of a plane
#* Find the equation of a plane in 3-space given a point and a normal vector, three points, or a geometric description of the plane.
#* Determine a normal vector and the intercepts of a given plane.
#* Represent a plane by parametric equations.
#* Find the distance from a point to a plane.
#* Find the angle between a line and a plane.
#* Determine a point of intersection between a line and a surface.
#* Sketch planes given their equations.
#* Solve application problems involving planes.
# Systems of Linear Equations
#* Define the following:
#** linear system of m equations in n unknowns
#** consistent and inconsistent
#** solution set
#** coefficient matrix
#** elementary row operations
#* Identify linear systems.
#* Represent a system of linear equations as an augmented matrix and vice versa.
#* Relate the following types of solution sets of a system of two or three variables to the intersections of lines in a plane or the intersection of planes in three space:
#** a unique solution.
#** infinitely many solutions.
#** no solution.
# Gaussian elimination
#* Define the following:
#** reduced row echelon form
#** leading variables or pivots
#** free variables
#** row echelon form
#** back substitution
#** Gaussian elimination
#** Gauss-Jordan elimination
#** homogeneous
#** trivial solution
#** nontrivial solutions
#* Identify matrices that are in row echelon form and reduced row echelon form.
#* Determine whether a linear system is consistent or inconsistent from its reduced row echelon form. If the system is consistent, write the solution.
#* Identify the lead variables and free variables of a system represented by an augmented matrix in reduced row echelon form.
#* Solve systems of linear equations using Gaussian elimination and back substitution.
#* Solve systems of linear equations using Gauss-Jordan elimination.
#* Model and solve application problems using linear systems.
# Matrices and Matrix Operations
#* Define the following:
#** vector, row vector, and column vector
#** equal matrices
#** scalar multiplication
#** sum of matrices
#** zero matrix
#** scalar product
#** linear combination
#** matrix multiplication
#** transpose
#** trace
#** identity matrix
#* Perform the operations of matrix addition, scalar multiplication, transposition, trace, and matrix multiplication.
#* Represent matrices in terms of double subscript notation.
# Inverses; Rules of Matrix Arithmetic
#* Define the following:
#** commutative property
#** singular
#** nonsingular or invertible
#** multiplicative inverse
#* Recall, demonstrate, and apply algebraic properties for matrices.
#* Recall that matrix multiplication is not commutative in general. Determine conditions under which matrices do commute.
#* Recall and prove properties and identities involving the transpose operator.
#* Recall and prove properties and identities involving matrix inverses.
#* Recall and prove properties and identities involving matrix powers.
#* Recall, demonstrate, and apply that the cancelation laws for scalar multiplication do not hold for matrix multiplication.
#* Recall and apply the formula for the inverse of 2x2 matrices.
# Elementary Matrices
#* Define the following:
#** elementary matrix
#** row equivalent matrices
#* Identify elementary matrices and find their inverses or show that their inverse does not exist.
#* Relate elementary matrices to row operations.
#* Factor matrices using elementary matrices.
#* Find the inverse of a matrix, if possible, using elementary matrices.
#* Prove theorems about matrix products and matrix inverses.
#* Solve a linear equation using matrix inverses.
# Further Results on Systems of Equations and Invertibility
#* Solve matrix equations using matrix algebra.
#* Recall and prove properties and identities involving matrix inverses.
#* Recall equivalent conditions for invertibility.
# Further Results on Systems of Equations and Invertibility
#* Define the following:
#** diagonal matrix
#** upper and lower triangular matrices
#** symmetric matrix
#** skew-symmetric matrix
#* Determine powers of diagonal matrices.
#* Recall and prove properties and identities involving the transpose operator.
#* Prove basic facts involving symmetric and skew-symmetric matrices.
# Determinants
#* Define the following:
#** minor
#** cofactor
#** cofactor expansion
#** determinant
#** adjoint
#** Cramer's Rule
#* Apply cofactor expansion to evaluate determinants of nxn matrices.
#* Recall and apply the properties of determinants to evaluate determinants.
#* Evaluate the adjoint of a matrix.
#* Determine whether or not a matrix has an inverse based on its determinant.
#* Evaluate the inverse of a matrix using the adjoint method.
#* Use Cramer's rule to solve a linear system.
# Properties of Determinants
#* Recall the effects that row operations have on the determinants of matrices. Relate to the determinants of elementary matrices.
#* Recall, apply and verify the properties of determinants to evaluate determinants, including:
#** det(AB) = det(A) det(B)
#** det(kA) = k^n det(A)
#** det(A^-1)= 1/det(A)
#** det(A^T) = det(A)
#** det(A) = 0 if and only if A is singular
#* Evaluate the determinant of a matrix using row operations.
#* Apply determinants to determine invertibility of matrix products.
# Linear Transformations: Definitions and Examples
#* Define the following:
#** linear transformation
#** image
#** range
#* Describe geometrically the effects of a linear operator.
#* Determine whether or not a given transformation is linear.
#* Prove theorems and solve application problems involving linear transformations.
# Matrix Representations of Linear Transformations
#* Define the following:
#** standard matrix representation
#** eigenvalues and eigenvectors
#* Determine the matrix that represents a given linear transformation of vectors given an algebraic description.
#* Determine the matrix that represents a given linear transformation of vectors given a geometric description.
#* Prove theorems and solve application problems involving linear transformations.
# Vector Spaces: Definitions and Examples
#* Define the following:
#** vector space
#** vector space axioms
#** vector space R^n
#** vector space R^(mxn)
#** vector space of real-valued functions
#** additional properties of vector spaces
#* Prove or disprove that a given set of vectors together with an addition and a scalar multiplication is a vector space.
#* Prove and verify properties of a vector space.
# Subspaces
#* Define the following:
#** subspace
#** closure under addition
#** closure under scalar multiplication
#** zero subspace
#** linear combination
#** span (or subspace spanned by a set of vectors)
#** spanning set
#* Prove or disprove that a set of vectors forms a subspace.
#* Prove or disprove a set of vectors is a spanning set for R^n.
#* Prove or disprove a given vector is in the span of a set of vectors. Determine the span of a set of vectors.
#* Prove theorems about vector spaces and spans.
# Linear Independence
#* Define the following:
#** linearly independent
#** linearly dependent
#** Wronskian
#* Determine whether a set of vectors is linearly dependent or linearly independent.
#* Geometrically describe the span of a set of vectors. For sets that are linearly dependent, determine a dependence relation.
#* Prove theorems about linear independence.
# Basis and Dimension
#* Define the following:
#** basis
#** dimension
#** finite and infinite dimensional
#** standard basis
#* Prove or disprove a set of vectors forms a basis.
#* Find a basis for a vector space.
#* Determine the dimension of a vector space.
#* Geometrically interpret the ideas of span, linear dependance, basis, and dimension.
# Row Space, Column Space, and Null Space
#* Define the following:
#** row space
#** column space
#** null space
#** particular solution
#** general solution
#* Express a product Ax as a linear combination of column vectors.
#* Find a basis for a the column space, the row space, and the null space of a matrix.
#* Find the basis for a span of vectors.
# Rank and Nullity
#* Define the following:
#** rank
#** nullity
#** The Consistency Theorem
#** equivalent statements of invertibility
#* Find the rank and nullity of a matrix.
#* Recall and prove identities involving rank and nullity
#* Recall and apply the Consistency Theorm
#* Recall and apply the equivalent statements of invertibility.
# Eigenvalues and Eigenvectors
#* Define the following:
#** eigenvalue or characteristic value
#** eigenvector or characteristic vector
#** characteristic polynomial or characteristic polynomial
#** equivalent statements of invertibility
#* Find the eigenvalues and eigenvectors of an nxn matrix.
#* Prove theorems and solve application problems involving eigenvalues and eigenvectors.
# Diagonalization
#* Define the following:
#** diagonalizable
#** algebraic multiplicity
#** geometric multiplicity
#* Determine whether or not a matrix is diagonalizable.
#* Find the diagonalization of a matrix, if possible.
#* Find powers of a matrix using the diagonalization of a matrix.
#* Prove theorems and solve application problems involving the diagonalization of matrices.
# Limit, Continuity, Vector Derivative; The Rules of Differentiation
#* Define the following:
#** scalar functions
#** vector functions
#** components of a vector function
#** plane curve or space curve
#** parametrization of a curve
#** limit of a vector function
#** a vector function continuous at a point
#** derivative of a vector function
#** a differentiable vector function
#** integral of a vector function
#* Graph a parametric curve.
#* Identify a curve given its parametrization.
#* Determine combinations of vector functions such as sums, vector products and scalar products.
#* Evaluate limits, derivatives, and integrals of vector functions.
#* Recall, derive and apply rules to combinations of vector functions for the following:
#** limits
#** differentiation
#** integration
#* Determine continuity of a vector-valued function.
#* Prove theorems involving limits and derivatives of vector-valued functions.
#* Solve application problems involving vector-valued functions.
# Curves; Vector Calculus in Mechanics
#* Define the following:
#** directed path
#** differentiable parameterized curve
#** tangent vector
#** tangent line
#** unit tangent vector
#** principal normal vector
#** normal line
#** osculation plane
#** force vector
#** momentum vector
#** angular momentum vector
#** torque
#* Find the tangent vector and tangent line to a curve at a given point.
#* Find the principle normal and normal line to a curve at a given point.
#* Determine the osculating plane for a space curve at a given point.
#* Reverse the direction of a curve.
#* Solve application problems involving curves.
#* Solve application problems involving force, momentum, angular momentum, and torque.
# Arc Length
#* Define the following:
#** arc length
#** arc length parametrization
#* Evaluate the arc length of a curve.
#* Determine whether a curve is arc length parameterized.
#* Find the arc length parametrization of a curve.
# Curvilinear Motion; Curvature
#* Define the following:
#** velocity vector function
#** speed
#** acceleration vector function
#** uniform circular motion
#** curvature
#** tangential component of acceleration
#** normal component of acceleration
#* Given the position vector function of a moving object, calculate the velocity vector function, speed, and acceleration vector function, and vice versa.
#* Calculate the curvature of a space curve.
#* Recall the formulas for the curvature of a parameterized planar curve or a planar curve that is the graph of a function. Apply these formulas to calculate the curvature of a planar curve.
#* Determine the tangential and normal components of acceleration for a given parameterized curve.
#* Solve application problems involving curvilinear motion and curvature.
# Functions of Several Variables; A Brief Catalogue of the Quadric Surfaces; Projections
#* Define the following:
#** real-valued function of several variables
#** domain
#** range
#** bounded functions
#** quadric surface
#** intercepts
#** traces
#** sections
#** center
#** symmetry
#** boundedness
#** cylinder
#** ellipsiod
#** elliptic cone
#** elliptic paraboloid
#** hyperboloid of one sheet
#** hyperboloid of two sheets
#** hyperbolic paraboloid
#** parabolic cylinder
#** elliptic cylinder
#** projection of a curve onto a coordinate plane
#* Describe the domain and range of a function of several variables.
#* Write a function of several variables given a description.
#* Identify standard quadratic surfaces given their functions or graphs.
#* Sketch the graph of a quadratic surface by sketching intercepts, traces, sections, centers, symmetry, boundedness.
#* Find the projection of a curve, that is the intersection of two surfaces, to a coordinate plane.
# Graphs; Level Curves and Level Surfaces
#* Define the following:
#** level curve
#** level surface
#* Describe the level sets of a function of several variables.
#* Graphically represent a function of two variables by level curves or a function of three variables by level surfaces.
#* Identify the characteristics of a function from its graph or from a graph of its level curves (or level surfaces).
#* Solve application problems involving level sets. functions.
# Partial Derivatives
#* Define the following:
#** partial derivative of a function of several variables
#** second partial derivative
#** mixed partial derivative
#* Interpret the definition of a partial derivative of a function of two variables graphically.
#* Evaluate the partial derivatives of a function of several variables.
#* Evaluate the higher order partial derivatives of a function of several variables.
#* Verify equations involving partial derivatives.
#* Apply partial derivatives to solve application problems.
# Open and Closed Sets; Limits and Continuity; Equity of Mixed Partials
#* Define the following:
#** neighborhood of a point
#** deleted neighborhood of a point
#** interior of a set
#** boundary of a set
#** open set
#** closed set
#** limit of a function of several variables at a point
#** continuity of a function of several variables at a point
#* Determine the boundary and interior of a set.
#* Determine whether a set is open, closed, neither, or both.
#* Evaluate the limit of a function of several variables or show that it does not exists.
#* Determine whether or not a function is continuous at a given point.
#* Recall and apply the conditions under which mixed partial derivatives are equal.
# Differentiability and Gradient
#* Define the following:
#** differentiable multivariable function
#** gradient of a multivariable function
#* Evaluate the gradient of a function.
#* Find a function with a given gradient.
# Gradient and Directional Derivative
#* Define the following:
#** directional derivative
#** isothermals
#* Recall and prove identities involving gradients.
#* Give a graphical interpretation of the gradient.
#* Evaluate the directional derivative of a function.
#* Give a graphical interpretation of directional derivative.
#* Recall, prove, and apply the theorem that states that a differential function f increases most rapidly in the direction of the gradient (the rate of change is then ||f(x)||) and it decreases most rapidly in the opposite direction (the rate of change is then -||f(x)||).
#* Find the path of a heat seeking or a heat repelling particle.
#* Solve application problems involving gradient and directional derivatives.
# The Mean-Value Theorem; The Chain Rule
#* Define the following:
#** the Mean Value Theorem for functions of several variables
#** normal line
#** chain rules for functions of several variables
#** implicit differentiation
#* Recall and apply the Mean Value Theorem for functions of several variables and its corollaries.
#* Apply an appropriate chain rule to evaluate a rate of change.
#* Apply implicit differentiation to evaluate rates of change.
#* Solve application problems involving chain rules and implicit differentiation.
# The Gradient as a Normal; Tangent Lines and Tangent Planes
#* Define the following:
#** normal vector
#** tangent vector
#** tangent line
#** tangent plane
#** normal line
#* Use gradients to find the normal vector and normal line to a smooth planar curve at a given point.
#* Use gradients to find the tangent vector and tangent line to a smooth planar curve at a given point.
#* Use gradients to find the normal vector to a smooth surface at a given point.
#* Use gradients to find the tangent plane to a smooth surface at a given point.
#* Use gradients to find the normal line to a smooth surface at a given point.
#* Solve application problems involving normals and tangents to curves and surfaces.
# Local Extreme Values
#* Define the following:
#** local minimum and local maximum
#** critical points
#** stationary points
#** saddle points
#** discriminant
#** Second Derivative Test
#* Find the critical points of a function of two variables.
#* Apply the Second-Partials Test to determine whether each critical point is a local minimum, a local maximum, or a saddle point.
#* Solve word problems involving local extreme values.
# Absolute Extreme Values
#* Define the following:
#** absolute minimum and absolute maximum
#** bounded subset of a plane or three-space
#** the Extreme Value Theorem
#* Determine absolute extreme values of a function defined on a closed and bounded set.
#* Apply the Extreme Value Theorem to justify the method for finding extreme values of functions defined on certain sets.
#* Solve word problems involving absolute extreme values.
# Maxima and Minima with Side Conditions
#* Define the following:
#** side conditions or constraints
#** method of Lagrange
#** Lagrange multipliers
#** cross-product equation of the Lagrange condition
#* Graphically interpret the method of Lagrange.
#* Determine the extreme values of a function subject to a side conditions by applying the method of Lagrange.
#* Apply the cross-product equation of the Lagrange condition to solve extreme value problems subject to side conditions.
#* Apply the method of Lagrange to solve word problems.
# Differentials; Reconstructing a Function from its Gradient
#* Define the following:
#** differential
#** general solution
#** particular solution
#** connected open set
#** open region
#** simple closed curve
#** simply connected open region
#** partial derivative gradient test
#* Determine the differential for a given function of several variables.
#* Determine whether or not a vector function is a gradient.
#* Given a vector function that is a gradient, find the functions with that gradient.
# Multiple-Sigma Notation; The Double Integral over a Rectangle R; The Evaluation of Double Integrals by Repeated Integrals
#* Define the following:
#** double sigma notation
#** triple sigma notation
#** upper sum
#** lower sum
#** double integral
#** integral formula for the volume of a solid bounded between a region Omega in the xy-plane and the graph of a non-negative function z = f(x,y) defined on Omega.
#** integral formula for the area of region in a plane
#** integral formula for the average of a function defined on a region Omega.
#** projection of a region onto a coordinate axis
#** Type I and Type II regions
#** reduction formulas for double integrals
#** the geometric interpretation of the reduction formulas for double integrals
#* Evaluate double and triple sums given their sigma notation.
#* Recall and apply summation identities.
#* Approximate the integral of a function by a lower sum and an upper sum.
#* Evaluate the integral of a function using the definition.
#* Evaluate double integrals over a rectangle using the reduction formulas.
#* Sketch planar regions and determine if they are Type I, Type II, or both.
#* Evaluate double integrals over Type I and Type II regions.
#* Change the order of integration of an integral.
#* Apply double integrals to calculate volumes, areas, and averages.
# The Double Integral as the Limit of Riemann Sums; Polar Coordinates
#* Define the following:
#** diameter of a set
#** Riemann sum
#** double integral as a limit of Riemann sums
#** polar coordinates (r; theta)
#** transformation formulas between Cartesian and polar coordinates
#** double integral conversion formula between Cartesian and polar coordinates
#* Represent a region in both Cartesian and polar coordinates.
#* Evaluate double integrals in terms of polar coordinates.
#* Evaluate areas and volumes using polar coordinates.
#* Convert a double integral in Cartesian coordinates to a double integral in polar coordinates and then evaluate.
# Further Applications of the Double Integral
#* Define the following:
#** integral formula for the mass of a plate
#** integral formulas for the center of mass of a plate
#** integral formulas for the centroid of a plate
#** integral formulas for the moment of an inertia of a plate
#** radius of gyration
#** the Parallel Axis Theorem
#* Evaluate the mass and center or mass of a plate
#* Evaluate the centroid of a plate.
#* Evaluate the moments of inertia of a plate.
#* Calculate the radius of gyration of a plate.
#* Recall and apply the parallel axis theorem.
# Triple Integrals; Reduction to Repeated Integrals
#* Define the following:
#** triple integral
#** integral formula for the volume of a solid
#** integral formula for the mass of a solid
#** integral formulas for the center of mass of a solid
#* Evaluate physical quantities using triple integrals such as volume, mass, center of mass, and moments of intertia.
#* Recall and apply the properties of triple integrals, including: linearity, order, additivity, and the mean-value condition.
#* Sketch the domain of integration of an iterated integral.
#* Change the order of integration of a triple integral.
# Cylindrical Coordinates
#* Define the following:
#** cylindrical coordinates of a point
#** coordinate transformations between Cartesian and cylindrical coordinates
#** cylindrical element of volume
#* Convert between Cartesian and cylindrical coordinates.
#* Describe regions in cylindrical coordinates.
#* Evaluate triple integrals using cylindrical coordinates.
# Spherical Coordinates
#* Define the following:
#** spherical coordinates of a point
#** coordinate transformations between Cartesian and spherical coordinates
#** spherical element of volume
#* Convert between Cartesian and spherical coordinates.
#* Describe regions in spherical coordinates.
#* Evaluate triple integrals using spherical coordinates.
# Jacobians; Changing Variables in Multiple Integration
#* Define the following:
#** Jacobian
#** change of variable formula for double integration
#** change of variable formula for triple integration
#* Find the Jacobian of a coordinate transformation.
#* Use a coordinate transformation to evaluate double and triple integrals.
# Line Integrals
#* Define the following:
#** work along a curved path
#** smooth parametric curve
#** directed or oriented curve
#** path dependence
#** closed curve
#* Evaluate the work done by a varying force over a curved path.
#* Evaluate line integrals in general including line integrals with respect to arc length.
#* Evaluate the physical characteristics of a wire such as centroid, mass, and center of mass using line integrals.
#* Determine whether or not a vector field is a gradient.
#* Determine whether or not a differential form is exact.
# The Fundamental Theorem for Line Integrals; Work-Energy Formula; Conservation of Mechanical Energy
#* Define the following:
#** path-independent line integrals
#** closed vector field
#** simply connected
#* Recall, apply, and verify the Fundamental Theorem for Line Integrals (Theorem 2 in Section 15.3).
#* Determine whether or not a force field is closed on a given region, and if so, find its potential function.
#* Solve application problems involving work done by a conservative vector field
# Vector Fields
#* Define the following:
#** vector field
#** open
#** path connected
#** region
#** integral curve (field lines, flow lines, or streamlines)
#** gradient vector field (or conservative vector field)
#** potential function
#** continuously differentiable vector field
#* Sketch a vector field.
#* Write the formula for a vector field from a description.
#* Write the gradient vector field associated with a given scalar-valued function.
#* Recover a function from its gradient or show it is not possible.
#* Find the integral curves of a vector field.
# Green's Theorem
#* Define the following:
#** Jordan curve
#** Jordan region
#** Green's Theorem
#* Recall and verify Green's Theorem.
#* Apply Green's Theorem to evaluate line integrals.
#* Apply Green's Theorem to find the area of a region.
#* Derive identities involving Green's Theorem
# Parameterized Surfaces; Surface Area
#* Define the following:
#** parameterized surface
#** fundamental vector product
#** element of surface area for a parameterized surface
#** surface integral
#** integral formula for the surface area of a parameterized surface
#** integral formula for the surface area of a surface z = f(x; y)
#** upward unit normal
#* parameterize a surface.
#* evaluate the fundamental vector product for a parameterized surface.
#* Calculate the surface area of a parameterized surface.
#* Calculate the surface area of a surface z = f(x; y).
# Surface Integrals
#* Define the following:
#** surface integral
#** integral formulas for the surface area and centroid of a parameterized surface
#** integral formulas for the mass and center of mass of a parameterized surface
#** integral formulas for the moments of inertia of a parameterized surface
#** integral formula for flux through a surface
#* Calculate the surface area and centroid of a parameterized surface.
#* Calculate the mass and center of mass of a parameterized surface.
#* Calculate the moments of inertia of a parameterized surface.
#* Evaluate the flux of a vector field through a surface.
#* Solve application problems involving surface integrals.
# The Vector Differential Operator Del
#* Define the following:
#** the vector differential operator Del
#** divergence
#** curl
#** Laplacian
#* Evaluate the divergence of a vector field.
#* Evaluate the curl of a vector field
#* Evaluate the Laplacian of a function.
#* Recall, derive and apply formulas involving divergence, gradient and Laplacian.
#* Interpret that divergence and curl of a vector fields physically.
# The Divergence Theorem
#* Define the following:
#** outward unit normal
#** the divergence theorem
#** sink and source
#** solenoidal
#* Recall and verify the Divergence Theorem.
#* Apply the Divergence Theorem to evaluate the flux through a surface.
#* Solve application problems using the Divergence Theorem.
# Stokes' Theorem
#* Define the following:
#** oriented surface
#** outward, upward, and downward unit normal
#** the positive sense around the boundary of a surface
#** circulation
#** component of curl in the normal direction
#** irrotational
#** Stokes' theorem
#* Recall and verify Stoke's theorem.
#* Use Stokes' Theorem to calculate the flux of a curl vector field through a surface by a line integral.
#* Apply Stokes' theorem to calculate the work (or circulation) of a vector field around a simple closed curve.




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=== Textbooks ===
Possible textbooks for this course include (but are not limited to):

*


=== Additional topics ===

=== Courses for which this course is prerequisite ===
[[Math 303 Mathematics for Engineering 2]]

[[Category:Courses|302 Mathematics for Engineering1]]