MAT2214

Topics List

Date	Sections	Topics	Prerequisite Skills	Student Learning Outcomes
Week 1	12.1	Three-Dimensional Coordinate Systems	One-dimensional coordinate systems Two-dimensional coordinate systems Algebraic Expressions Solving Inequalities Distance Formula in the Plane	Three-dimensional coordinate systems Distance Formula in R3 Standard Equation for a Sphere
Week 1/2	12.2	Vectors	Line Segments Length of a Line	Vector Algebra Operations Magnitude of a vector Unit Vectors Midpoint of a Line Segment Angle between vectors Definition of Dot product Orthogonal vectors Vector projection
Week 2	12.3	The Dot Product	Basic Trig Functions Customary domain restrictions for Trigonometric Functions Vectors Midpoint Formula	Find the area of plane regions bounded by the graphs of functions.
Week 2/3	12.4	The Cross Product	Basic Trig Functions The Dot Product Determinants	Define the cross product Properties of the cross product Area of a parallelogram Cross product as a determinant
Week 3	12.5	Cylinders and Quadratic Surfaces	Quadratic Functions Parametric Equations Conics	Find equations for cylinders that are generated by rotating lines that are parallel to a plane Understand basic quadratic surfaces Understand general quadratic surfaces
Week 3/4	13.1	Curves in Space and Vector Functions	Parametric Equations Vectors The Derivative as a Function The Limit of a Function Continuity The Dot Product The Cross Product	Vector functions Limits of vector functions Continuity of vector functions Differentiation of vector functions Differentiation rules for vector functions Curves and paths in space
Week 4	13.2	Integrals of Vector Functions	Initial Value Problems Solving Basic Integrals Parametric Equations Vector Functions	Indefinite integrals of vector functions Definite integrals of vector functions Vector and parametric equations for ideal projectile motion
Week 4/5	13.3	Arc Length	Length of a Line Vector Functions Integrals of Vector Functions	Length of a curve in R3 General arc length formula Arc length for parameterized curves The Unit tangent vector
Week 5	13.4	Curvature and Normal Vectors	Antiderivatives Vectors Parametric Equations The Unit Tangent Vector Conics	Curvature in R2 Formula for curvature Definition of Principal unit normal Curvature and normal vectors for higher dimensions.
Week 5/6	13.5	Tangential and Normal Components of Acceleration	The Cross Product Derivatives of Vector Functions Curvature and Normal Vectors Determinants	Binormal Vectors Definition of tangential and normal components of acceleration Torsion
Week 7	14.1	Functions of Several Variables	Domain of a Function Range of a Function Interval Notation Graphing a Function Equation of a Circle	Domain and range of multivariable functions Functions with two variables Bounded regions Graphs and level curves of two variable functions Functions of three variables Level surfaces
Week 7/8	14.2	Limits and Continuity in Higher Dimensions	The Limit of a Function Continuity The Limit Laws Composition of Functions The Dot Product The Cross Product	Limits of functions of two variables Properties of limits of functions of two variables Continuity for functions of two variables Continuity of composition Functions of more than two variables Extreme values on closed and bounded sets
Week 8	14.3	Partial Derivatives	Second derivatives Limits and Continuity in Higher Dimensions Functions of Several Variables	Partial derivatives for functions of two variables Partial derivatives for functions of more than two variables Partial derivatives and continuity Second order partial derivatives Mixed derivative theorem Define the derivative for functions of two variables
Week 8/9	14.4	The Chain Rule for Functions of more than One Variable	Differentiation Rules The Chain Rule Implicit Differentiation Parametric Equations Partial Derivatives	Chain rule for functions of one independent variable and two intermediate variables. Chain rule for functions of one independent variable and three intermediate variables. Chain rule for functions of two independent variable and two intermediate variables. Additional method for implicit differentiation. The general chain rule
Week 9	14.5	Directional Derivatives and Gradient Vectors	Trigonometric Functions The Chain Rule for Functions of more than One Variable Unit Vectors Partial Derivatives The Dot Product	Direction Derivatives in the plane Gradients Properties of directional derivatives Tangents to level curves Directional derivatives for functions of three variables The chain rule for paths
Week 9/10	14.6	Tangent Planes and Differentials	Linear Approximations and Differentials Parametric Equations Partial Derivatives Slope of a Line Cylinders and Quadratic Surfaces	Tangent Planes and Normal lines The plane tangent to a surface How to linearize a function of two variables Differentials for functions of two variables Linearization and differentials for functions of more than two variables
Week 10	14.7	Extreme Values and Saddle Points	Extreme values on closed and bounded sets Partial Derivatives Critical Points of a Function Continuity of functions with two variables	The derivative test for local extreme values Critical points and saddle points for functions of two variables Second derivative test for local extreme values Absolute maxima and minima on closed and bounded regions
Week 10/11	14.8	Lagrange Multipliers	Extreme Values and Saddle Points Cylinders and Quadratic Surfaces Directional Derivatives and Gradient Vectors	Define the convergence or divergence of an infinite series. Find the sum of a geometric or telescoping series.
Week 12	14.9	Taylors formula for Two Variables	Taylor and Maclaurin Series Partial Derivatives Limits and Continuity in Higher Dimensions	The derivation of the second derivative test Taylor's formula for functions of two variables
Week 12/13	15.1	Double and Iterated Integrals over Rectangles	Approximating Areas Limits of Riemann Sums	Double Integrals Fubini's Theorem (part 1)
Week 14	15.2	Double Integrals over General Regions	Continuity Determining Volumes by Slicing Double and Iterated Integrals over Rectangles	Double integrals over bounded, nonrectangular regions Volumes of solid regions Fubini's theorem (part 2) Finding the limits of integration for regions in the plane Properties of double Integrals
Week 14/15	15.3	Area by Double Intgration	Double Integrals over General Regions Average value of a fucntion Conics	Areas of bounded regions in the plane Average value for functions of two or more variables
Week 15	15.4	Double Integrals in Polar Form	Double Integrals over General Regions Polar Coordinates	Integrals in Polar Form Finding limits of integration for polar coordinates Changing Cartesian Integrals into Polar Integrals
Week 15/16	15.5	Triple Integrals in Rectangular Coordinates	Double and Iterated Integrals over Rectangles Area by Double Integration Change of Variables	Triple Integrals Volume of a region in space Finding the limits of integration for triple integrals Average value of a function in space
Week 16	15.6	Applications of Double and Triple Integrals	Moments and Center of Mass Triple Integrals in Rectangular Coordinates Partial Derivatives	Masses and First moments Moments of Inertia
Week 16/17	15.7	Triple Integrals in Cylindrical and Spherical Coordinates	Double Integrals in Polar Form Polar Form Triple Integrals in Rectangular Coordinates	Integration in Cylindrical Coordinates Equations relating rectangular and cylindrical coordinates Spherical coordinates and integrations Equations relating spherical coordinates to Cartesian and cylindrical coordinates
Week 17	16.1	Line Integrals of Scalar Functions	Parametric Equations Curves in Space and Vector Functions Arc Length	Evaluating a Line Integral Additivity of Line Integrals Mass and Moments Line Integrals in the plane
Week 18	16.2	Vector Fields and Line Integrals	The Dot Product Directional Derivatives and Gradient Vectors Parametric Equations Line Integrals of Scalar Functions	Vector Fields Gradient Fields Line Integrals of vector fields Line integrals with respect to each components direction Work done by a force over a curve in space Flow integrals and circulation for velocity fields Flux across a simple closed plane curve
Week 18/19	16.3	Path Independence and Conservation Fields	Vector Fields and Line Integrals Partial Derivatives Gradient Fields Tangent Planes and Differentials	Path Independence Piecewise smooth curves and connected domains in open regions Line integrals in Conservation fields Finding potentials for conservative fields Exact Differential forms
Week 20	16.4	Green's Theorem	Vector Fields and Line Integrals Partial Derivatives Dot Product Path Independence and Conservation Fields	Circulation Density Divergence (flux density) of a vector field The two forms of Green's theorem (Tangential and Normal forms) Green's theorem for evaluating line integrals
Week 21	16.5	Surfaces and Area	Vector Fields and Line Integrals Partial Derivatives The Cross Product Parametric Equations Integration Techniques Double Integrals over General Regions	Parameterizations of Surfaces Surface Area Surface Area Differential for a Parameterized Surface Implicit Surfaces