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Calculus III


Syllabus (the latest semester) 



Contents

  • Chapter 12: Vectors and geometry of space

    • 12.1 Three dimensional coordinate system

    • 12.2 Vectors

    • 12.3 The dot product

    • 12.4 The cross product

    • 12.5 Equations of lines and planes

    • 12.6 Quadratic surfaces

  • Chapter 13: Vector functions

    • 13.1 Vector functions and space curves

    • 13.2 Derivatives and integrals of vector functions

    • 13.3 Arc length and curvature

    • 13.4 Motion in space: velocity and acceleration

  • Chapter 14: Functions of several variables, partial derivatives

    • 14.1 Functions of several variables

    • 14.2 Limits and continuity

    • 14.3 Partial derivatives

    • 14.4 Tangent planes and linear approximation

    • 14.5 The chain rule

    • 14.6 Directional derivatives and the gradient

    • 14.7 Maximum and minimum values

    • 14.8 Lagrange multipliers

    • 14.9 Taylor series for functions of several variables* (not in the book)

  • Chapter 15: Multiple integrals

    • 15.1 Double integrals over rectangles

    • 15.2 Iterated integrals

    • 15.3 Double integrals over general regions

    • 15.4 Double integrals in polar coordinates

    • 15.5 Applications of double integrals

    • 15.6 Surface area

    • 15.7 Triple integrals

    • 15.8 Triple integrals in cylinder coordinates

    • 15.9 Triple integrals in spherical coordinates

    • 15.10 Change of variables in multiple integrals

  • Chapter 16: Vector Calculus

    • 16.1 Vector fields

    • 16.2 Line integrals

    • 16.3 The fundamental theorem of line integrals

    • 16.4 Green's theorem

    • 16.5 Curl and divergence

    • 16.6 Parametric surfaces and their areas

    • 16.7 Surface integrals

    • 16.8 Stoke's theorem

    • 16.9 The divergence theorem


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