On successful completion of this subject, students should be able to:

1. Define i and operate with complex numbers.
2. Define and manipulate the following functions: exponential, trigonometric, hyperbolic, logarithmic, inverse trig and inverse hyperbolic.
3. Find limits of functions and determine if a function is continuous or differentiable.
4. Find the derivatives of functions.
5. Apply correctly techniques of differential calculus to problems involving optimization, curve sketching and rates of change.
6. Calculate basic integrals.

- Functions and Inverse Functions: Functions and their Graphs; Trigonometric, Exponential, and Hyperbolic Functions; Inverse Functions; Logarithmic Functions; Inverse Trigonometric and Hyperbolic Functions.
- Complex Numbers: Definition; Basic Operations; Argand Diagram; Polar Form; Euler's Formula; De Moivre's Theorem; Powers and Roots.
- Limits and Continuity: Limit of a Function; Limit Laws; One-Sided Limits; Limits at Infinity; The Sandwich Theorem; Vertical and Horizontal Asymptotes; Intermediate Value Theorem.
- Differentiation: Definition of the Derivative; Differentiability implies Continuity; Derivatives of Polynomials and Exponential Functions; Product and Quotient Rules; Chain Rule; Implicit Differentiation; Derivatives of Trigonometric and Hyperbolic Func
- Applications of Derivatives: Maximum and Minimum Values; Extreme Value Theorem; Roll's Theorem and the Mean Value Theorem; Monotonic Functions and the First Derivative Test; Concavity and Curve Sketching; Applied Optimization; Indeterminate Forms an' L'
- Integration: Antiderivatives; Indefinite and Definite Integrals; Connection between the Definite and Indefinite Integrals.