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. Intermediate Value Theorem
3. Derivatives
   1. Idea
   2. Definition
   3. Calculating a derivative using the definition (Very simple)
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. Products, dot and cross
   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