Course info

Course Aim: Develop students’ practical skills in differential calculus of single variable functions.
Main Topics: Types of functions, curve sketching using shifts, reflections, and scaling for: polynomials, radical functions, equation of the straight line, exponential functions and logarithmic function. Solving equations involving exponentials and logarithms- Trig functions and inverse trig functions- Hyperbolic functions and Inverse Hyperbolic functions- Limits and Continuity- Differentiation using definition and rules- Derivatives of inverse trig and hyperbolic functions- Higher order derivatives- Logarithmic differentiation- Implicit differentiation- Linear approximation- L’Hopital’s Rule- Absolute and Local Extrema- Monotonicity and Concavity of a function- Optimization- Introducing the concept of Antiderivative, indefinite integral, basic rules of integration- Definite integrals and Fundamental Theorem of Calculus- Integration by substitution- Application to integration: Area bounded between curves