Math 1700

Fall 2022

Topics and Skills

Mobius Strip

By the end of the class students should be able to do or explain the following:

  1. Vectors
    1. Sums
    2. Dot product
    3. Geometric interpretations
    4. Projections
    5. Vector valued functions
    6. Harmonic motion
  2. Know the basic definitions and concepts behind the following:
    1. Limits
    2. Derivatives
    3. Definite integrals
    4. Antiderivatives
  3. Limits
    1. Idea
    2. Definition
    3. Computing limits
    4. Continuous functions
    5. Intermediate Value Theorem
  4. Derivatives
    1. Idea
    2. Definition
    3. Calculating a derivative using the definition (Simple cases only.)
  5. Differentiation techniques and formulas
    1. Powers and polynomials
    2. Trigonometric function
    3. Products and quotients
    4. Compositions, chain rule
    5. Implicit differentiation
    6. Vector valued functions
  6. Approximations using derivatives
    1. Tangent lines
    2. Linear approximations
    3. Newton's method
    4. Mean Value Theorem
    5. Taylor polynomials
  7. Inverse trigonometric functions
    1. Definitions and graphs
    2. Evaluation of inverse trigonometric functions
    3. Derivatives of inverse trigonometric functions
  8. Related rates
    1. Formulate and solve problems that relate the change between different quantities.
  9. Minimization and maximization
    1. Critical points
    2. Local and global optimal points
    3. Second order conditions
      1. Quadratic approximations
    4. Applications to applied problems
  10. Numerical methods
    1. Newton's method
    2. Riemann sums
    3. Estimating with linear approximations
  11. Integrals
    1. Definition of the antiderivative
    2. Simple antiderivatives
    3. Substitution
    4. Definite integrals and area
    5. Fundamental Theorem of Calculus
  12. Differential equations
    1. Definition
    2. Definition of a solution
    3. Solving differential equations using antiderivatives
  13. Calculators
    1. Know how to work without a calculator
    2. Using a calculator for numerical calculations
  14. Clearly write out assignments
  15. Be able to work multistep problems
  16. Improve algebra skills

 

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Jay Treiman: jay.treiman at wmich.edu