Learning Outcomes At the end of the course the student should be able to:
- (Limits and continuity) Evaluate limits analytically, graphically, and numerically, and use limits to investigate properties of functions such as continuity and existence of asymptotes. Investigate continuity properties of functions.
- (Derivatives) Define and evaluate the derivative at a point as a limit using limits, numerical, graphical methods. Investigate differentiability of a function at a point using limits, numerical, or graphical methods.
- (Computing derivatives algebraically) Compute first and higher order derivatives algebraically by applying theorems. Compute derivatives of functions defined implicitly.
- (Using Derivatives) Apply differentiation to investigate velocity, acceleration, related rates, monotonicity, optimization problems, linear approximation, limits (L’Hopital’s rule), and functions defined parametrically. Apply theorems about continuous and differentiable functions (Extreme Value Theorem, Mean Value Theorem).
- (Integration) Use Riemann sums to approximate integrals. Use the First and Second Fundamental Theorem of Calculus to compute integrals of simple functions, and apply them to total change. Use integrals to compute area of planar regions bounded by simple functions.
- (Modeling, Approximation, Technology use) Use calculus and technology to investigate mathematical models and determine their applicability. Use technology to study accuracy of approximations, perform numerical and symbolic calculations, and produce graphical representations of functions to investigate their properties.