For students who are already fluent with single-variable derivatives and integrals, this workbook offers practice with essential skills from multivariable calculus (including vector calculus ). Each chapter begins with a review of the essential ideas and includes fully solved examples to help serve as a guide. The full solution to every exercise can be found at the back of the book. Authored by experienced teacher, Chris McMullen, Ph.D., this self-study math workbook covers: partial derivatives extreme values with multiple variables (including saddle points) vectors, vector analysis (such as the dot and cross products), and vector calculus the gradient, divergence, and curl the main coordinate systems: Cartesian, 2D polar, spherical, and cylindrical path integrals, surface integrals, and volume integrals flux integrals, center of mass, and moment of inertia tangent and normal vectors and more The author, Chris McMullen, Ph.D., has over twenty years of experience teaching math skills to physics students. He prepared this workbook of the Improve Your Math Fluency series to share his strategies for solving calculus problems with multiple variables or vectors. For students who are already fluent with single-variable derivatives and integrals, this workbook offers practice with essential skills from multivariable calculus (including vector calculus). Each chapter begins with a review of the essential ideas and includes fully solved examples to help serve as a guide. The full solution to every exercise can be found at the back of the book. Authored by experienced teacher, Chris McMullen, Ph.D., this self-study math workbook covers: partial derivatives, extreme values with multiple variables (including saddle points), vectors, vector analysis (such as the dot and cross products), vector calculus, the gradient, divergence, the curl, the main coordinate systems (Cartesian, 2D polar, spherical, and cylindrical), path integrals, surface integrals, volume integrals, flux integrals, center of mass, moment of inertia, tangent and normal vectors, and more. The author, Chris McMullen, Ph.D., has over twenty years of experience teaching math skills to physics students. He prepared this workbook of the Improve Your Math Fluency series to share his strategies for solving calculus problems with multiple variables or vectors. Contents Introduction 1. Partial Derivatives 2. The Chain Rule with Multiple Variables 3. Extreme Values with Multiple Variables 4. Vectors 5. Scalar and Vector Products 6. Polar Coordinates 7. Spherical Coordinates 8. Cylindrical Coordinates 9. The Gradient 10. The Divergence 11. The Curl 12. Normal and Tangent Vectors 13. Line Integrals 14. Surface and Volume Integrals 14. Surface and Volume Integrals 15. Center of Mass and Moment of Inertia Solutions Solutions Chapter1 Solutions Chapter2 Solutions Chapter3 Solutions Chapter4 Solutions Chapter5 Solutions Chapter6 Solutions Chapter7 Solutions Chapter8 Solutions Chapter9 Solutions Chapter10 Solutions Chapter11 Solutions Chapter12 Solutions Chapter13 Solutions Chapter14 Solutions Chapter15
