Math 1700

Spring 2018

Topics and Skills

Mobius Strip

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

  1. Know the basic definitions and concepts behind the following:
    1. Limits
    2. Derivatives
    3. Definite integrals
    4. Antiderivatives
  2. Limits
    1. Idea
    2. Definition
    3. Computing limits
    4. Intermediate Value Theorem
  3. Derivatives
    1. Idea
    2. Definition
    3. Calculating a derivative using the definition (Simple cases only.)
  4. 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
  5. Approximations using derivatives
    1. Tangent lines
    2. Linear approximations
    3. Newton's method
    4. Mean Value Theorem
  6. Vectors
    1. Sums
    2. Dot product
    3. Geometric interpretations
    4. Projections
    5. Vector valued functions
    6. Harmonic motion
  7. Minimization and maximization
    1. Critical points
    2. Local and global optimal points
    3. Second order conditions
      1. Quadratic approximations
  8. Numerical methods
    1. Newton's method
    2. Riemann sums
    3. Estimating with linear approximations
  9. Integrals
    1. Definition of the antiderivative
    2. Simple antiderivatives
    3. Substitution
    4. Definite integrals and area
    5. Fundamental Theorem of Calculus
  10. Differential equations
    1. Definition
    2. Definition of a solution
    3. Solving differential equations using antiderivatives
  11. Calculators
    1. Know how to work without a calculator
    2. Using a calculator for numerical calculations
  12. Clearly write out assignments

 

Jay Treiman: jay.treiman at wmich.edu