Calculus 3 Multivariable Calculus Lectures and Problems
Edition: 7
Copyright: 2026
Pages: 362
Edition: 7
Copyright: 2026
Pages: 362
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This workbook covers the third semester of a traditional calculus course - Multivariable Calculus. The workbook follows the chapters in Stewart's Calculus and can be used as a supplement to Stewart or as a stand alone workbook. Topics covered include lines, planes, graphing, curves, partial derivatives, multiple integrals, change of variables, vector fields, and vector calculus.
Introduction
0.1: Introduction to Multivariable Calculus
0.2: Introduction to the Workbook
0.3: College Learning vs. High School Learning
0.4: Do these to succeed in this course
0.5: Some Resources. Use These!
0.6: AI in Mathematics Courses
Chapter 1: The Geometry of R3
1.1: Basic Graphing in R 3
1.2: Some Geometry and Topology in R 3
1.3: Graphing and Slices
1.4: Vectors and Lines
1.5: Dot Products, Angles, Projections, Matrices
1.6: Determinants, Cross Products and Planes
Chapter 2: Parametric Curves and Surfaces
2.1: Parametric Curves
2.2: Calculus of Curves and Scalar Line Integrals
2.3: Coordinates: Polar, Cylindrical, Spherical
2.4: Parametric Surfaces
Chapter 3: Differential Calculus of Multivariable Functions
3.1: Tangent Planes and Approximations
3.2: Chain Rule
3.3: Directional Derivatives
3.4: Local Extrema
3.5: Global Extrema
3.6: Lagrange Multipliers
Chapter 4: Integral Calculus of Multivariable Functions
4.1: Double and Triple Integrals over Rectangular Regions
4.2: Double Integrals over General Regions
4.3: Triple Integrals over General Regions
4.4: Change of Variables
4.5: Polar and Cylindrical Coordinates
4.6: Spherical Coordinates
4.7: Surface Area and Surface Integrals
Chapter 5: Vector Calculus
5.1: Vector Fields
5.2: Vector Line Integrals and Work
5.3: Fundamental Theorem and Independence of Path
5.4: Surface Integrals of a Vector Field, Flux Integrals
5.5: Stokes’ Theorem
5.6: Green’s Theorem: Stokes’ Theorem for the Plane
5.7: Divergence Theorem
5.8 Fundamental Theorem of Calculus
Associate Director of Undergraduate Studies and Teaching Professor of Mathematics at Washington University
This workbook covers the third semester of a traditional calculus course - Multivariable Calculus. The workbook follows the chapters in Stewart's Calculus and can be used as a supplement to Stewart or as a stand alone workbook. Topics covered include lines, planes, graphing, curves, partial derivatives, multiple integrals, change of variables, vector fields, and vector calculus.
Introduction
0.1: Introduction to Multivariable Calculus
0.2: Introduction to the Workbook
0.3: College Learning vs. High School Learning
0.4: Do these to succeed in this course
0.5: Some Resources. Use These!
0.6: AI in Mathematics Courses
Chapter 1: The Geometry of R3
1.1: Basic Graphing in R 3
1.2: Some Geometry and Topology in R 3
1.3: Graphing and Slices
1.4: Vectors and Lines
1.5: Dot Products, Angles, Projections, Matrices
1.6: Determinants, Cross Products and Planes
Chapter 2: Parametric Curves and Surfaces
2.1: Parametric Curves
2.2: Calculus of Curves and Scalar Line Integrals
2.3: Coordinates: Polar, Cylindrical, Spherical
2.4: Parametric Surfaces
Chapter 3: Differential Calculus of Multivariable Functions
3.1: Tangent Planes and Approximations
3.2: Chain Rule
3.3: Directional Derivatives
3.4: Local Extrema
3.5: Global Extrema
3.6: Lagrange Multipliers
Chapter 4: Integral Calculus of Multivariable Functions
4.1: Double and Triple Integrals over Rectangular Regions
4.2: Double Integrals over General Regions
4.3: Triple Integrals over General Regions
4.4: Change of Variables
4.5: Polar and Cylindrical Coordinates
4.6: Spherical Coordinates
4.7: Surface Area and Surface Integrals
Chapter 5: Vector Calculus
5.1: Vector Fields
5.2: Vector Line Integrals and Work
5.3: Fundamental Theorem and Independence of Path
5.4: Surface Integrals of a Vector Field, Flux Integrals
5.5: Stokes’ Theorem
5.6: Green’s Theorem: Stokes’ Theorem for the Plane
5.7: Divergence Theorem
5.8 Fundamental Theorem of Calculus
Associate Director of Undergraduate Studies and Teaching Professor of Mathematics at Washington University