Course syllabus

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Topics Theory

Adams, R. A. and Essex, C. (2021). Calculus: A Complete Course. 10th ed. Toronto: Pearson

 Homework 

Adams, R. A. and Essex, C. (2021). Calculus: A Complete Course. 10th ed. Toronto: Pearson
  • definition complex numbers
  • the complex plane
  • calculating with complex numbers
  • de Moivre's theorem
  • roots of complex numbers
  • complex powers of LaTeX: e
  • complex polynomials (optional for pre-master students)
  • the fundamental theorem of algebra (optional for pre-master students)
  • homogeneous second-order linear differential equations with constant coefficients
  • inhomogeneous second order linear differential equations with constant coefficients
    • § 3.7: Second Order Linear DEs with Constant Coefficients
    • § 19.4: Differential Equations of Second Order (Adams 9th ed. § 18.4)
    • § 19.5: Linear Differential Equations with Constant Coefficients, until p. 1041, not including Euler (Equidimensional) Equations. (Adams 9th ed. § 18.5) (Optional) 

This section regarding the Constant-Coefficient Equations of Higher Order is optional and will not be examined. Nevertheless, it is recommended to students for self-study in order to understand differential equations thoroughly.

    • § 19.6: Nonhomogeneous Linear Equations, until p. 1046, not including Resonance. (Adams 9th ed. § 18.6)
    • § 19.6: Nonhomogeneous Linear Equations p. 1047-1049 Variation of Parameters (Adams 9th ed. § 18.6) (Optional)

This section regarding the Variation of Parameters method is optional and will not be examined. Nevertheless, it is recommended to students for self-study in order to understand differential equations thoroughly.

  
  • § 3.7: 1, 3, 5, 8, 9, 11, 13, 15, 19-23
  • § 19.4: 1, 3
  • § 19.5: Optionally: 1-6
  • § 19.6: 1, 3, 4, 5, 7, 9, 11. Optionally: 13, 14
  • vectors, lines and planes
  • § 10.1: Analytic Geometry in Three Dimensions
  • § 10.2: Vectors
  • § 10.3: The Cross Product in 3-Space
  • § 10.4: Planes and Lines
  • § 10.1: 3, 7, 11, 15, 17, 31
  • § 10.2: 5, 10, 15, 29
  • § 10.4: 3, 7, 11
  • functions of more variables
  • limits and continuity
  • § 13.1: Functions of Several Variables (Adams 9th ed. § 12.1)
  • § 13.2: Limits and Continuity (Adams 9th ed. § 12.2)

  • § 13.1: 1, 3, 5, 15, 21, 23, 37
  • § 13.2: 1, 7, 11, 14, 22
  • partial derivatives
  • higher derivatives
  • the chain rule
  • linear approximation
  • gradient and directional derivative
  • § 13.3: Partial Derivatives (Adams 9th ed. § 12.3)
  • § 13.4: Higher-Order Derivatives (Adams 9th ed. § 12.4)
  • § 13.5: The Chain Rule (Adams 9th ed. § 12.5)
  • § 13.6: Linear Approximations, Differentiability, and Differentials (Adams 9th ed. § 12.6)
  • § 13.7: Gradients and Directional Derivatives (Adams 9th ed. § 12.7)
  • § 13.3: 1, 4, 9, 11
  • § 13.4: 1, 6, 7, 9, 15, 17, 23
  • § 13.5: 1, 2, 3, 5, 6, 16, 21
  • § 13.6: 1, 2, 3, 5, 6, 10, 11, 13
  • § 13.7: 4, 5, 7, 19, 22
  • application of the partial derivatives
  • extrema of a function under side conditions
  • the method of Lagrange multipliers

This entire topic is optional for pre-master students
  • § 14.1: Extreme Values (Adams 9th ed. § 13.1) 
  • § 14.2: Extreme Values of Functions Defined on Restricted Domains (Adams 9th ed. § 13.2) 
  • § 14.3: Lagrange Multipliers (Adams 9th ed. § 13.3) 
  • § 14.1: 1, 2, 3, 4, 5, 7, 19, 22
  • § 14.2: 1, 3, 7, 9, 11, 15
  • § 14.3: 1, 2, 3(b, c), 4, 6, 8, 9
  • double integrals
  • double integrals in polar coordinates
  • triple integrals
  • triple integrals in cylindrical coordinates
  • triple integrals in spherical coordinates
  • § 15.1: Double Integrals (Adams 9th ed. § 14.1)
  • § 15.2: Iteration of Double Integrals in Cartesian Coordinates (Adams 9th ed. § 14.2)
  • § 15.4: Double Integrals in Polar Coordinates (Adams 9th ed. § 14.4)
  • § 15.5: Triple Integrals (Adams 9th ed. § 14.5)
  • § 15.6: Change of Variables in Triple Integrals (Adams 9th ed. § 14.6)
  • § 15.1: 13, 14, 15, 16
  • § 15.2: 1, 4, 9, 11, 13, 15, 16, 19, 21, 23
  • § 15.4: 1, 3, 5, 8, 9, 11, 12
  • § 15.5: 1, 2, 4, 11, 14, 17, 20, 27
  • § 15.6: 2, 3, 4, 6, 11, 12, 13, 14
  • vector functions 
  • parametrised curves
  • vector field
  • field lines
  • conservative vector field

This entire topic is optional for pre-master students
  • § 12.1: Vector Functions of One Variable (Adams 9th ed. § 11.1)
  • § 12.3: Curves and Parametrizations (Adams 9th ed. § 11.3)
  • § 16.1: Vector and Scalar Fields (Adams 9th ed. § 15.1)
  • § 16.2: Conservative Fields (Adams 9th ed. § 15.2)
  • § 12.1: 1, 3, 5, 15, 17, 19
  • § 12.3: 1, 3, 5, 7, 11, 13
  • § 16.1: 
  • § 16.2: 1, 2, 3, 5, 7, 9, 10 (ex. 9, 10 no field lines have to be determined)
  • line integrals 
  • line integrals of vector fields 

This entire topic is optional for pre-master students
  • § 16.3: Line Integrals (Adams 9th ed. § 15.3)
  • § 16.4: Line Integrals of Vector Fields (Adams 9th ed. § 15.4)
  • § 16.3: 1, 2, 4, 5
  • § 16.4: 1, 3, 5, 7, 10, 12

Course summary:

Course Summary
Date Details Due