Multivariable Calculus
Peter Koroteev, UC Berkeley
Summer Course Format:
Eight hours of lecture and two hours of discussion per week.
Description: In this course we will study functions in several variables and operations on them, such as integration and partial differentiation, as well as their myriad applications.
Textbook: Stewart, Multiple Variable Calculus (8th edition)
Outline of the Course:
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Week 1
:Parametric equation curves, Calculus with parametric
equations, Polar coordinates, Areas and lengths in Polar
coordinates, Conic sections.
Videos of lectures: [Introduction, Dimensions, Parametric Curves] [Derivatives, Tangent Lines] [Arc Length, Areas of Rotational Surfaces] [Areas, Polar Coordinates, Conical Sections] [Discussion] iPad lecture notes: [Week 1] |
Chapter 10
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Week 2 : Three-dimensional coordinate systems, vectors, the dot products, the cross products, equations of lines and planes, cylinders and quadric surfaces, cylindrical and spherical coordinates. Videos of lectures: [3D Coordinate Systems, Vectors] [Dot Product, Cross Product] [Triple Product] [Applications, Quadratic Surfaces] iPad lecture notes: [Week 2] [Homework 1] [Quiz 1] |
Chapter 12
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Week 3 : Derivatives and integrals of vector functions, Arclength, Curvature, Motion in space. Videos of lectures: [Derivatives of Vector Functions] [Curvature, Torsion, Frenet Triple, Motion of Paricles] [Kepler Laws, Review] [Discussion, Review] [Discussion] iPad lecture notes: [Week 3] [Homework 2] [Quiz 2] |
Chapter 13
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Week 4 : Functions of several variables, Limits, Partial derivatives, Tangent lines Chain Rule, Gradient vector, Maximum and Minimum. Videos of lectures: [Functions of Several Variables, Limits and Continuity] [Partial Derivatives, Tangent Planes, Differentiability, Chain Rule] [Implicit Differentiation, Directional Derivatives, Gradient] [Review] [Discussion] iPad lecture notes: [Week 4] [Homework 3] [Quiz 3] |
Sections 14.1-14.6
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Week 5 : Maximum and Minimum, Lagrange Multipliers. Midterm Videos of lectures: [Minimum and Maximum] [Lagrange Multipliers] [Discussion] iPad lecture notes: [Week 5] [Homework 4] [Midterm] |
Sections 14.7-14.8
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Week 6 : Double Integrals, Surface Areas, Triple Intetgrals, Volumes. Videos of lectures: [Double Integrals] [Double Integrals in polar coordinates, Applications] [Physics applications, Triple Integrals, Cylindrical coordinates] [Discussion] iPad lecture notes: [Week 6] [Homework 5] [Quiz 4] |
Chapter 15
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Weeks 7,8 : Line integrals of vector fields, Green's theorem, differential forms, Parametric Surfaces, Areas, Orientation. Final 8/14 Videos of lectures: [Vector Fields, Line Integrals] [Line Integrals of Vector Fields] [Green's Theorem, Curl and Divergence] [Green's Theorem in Differential Form] [Divergence Theorem, Orientation] iPad lecture notes: [Week 7] [Week 8] [Homework 6] [Quiz 5] |
Chapter 16
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Preparation Materials: Math 53 [Worksheet] Archive of exams and midterms on [Tau Beta Pi]