This course has two main goals:

• Learning how to do explicit calculations
• Discovering some fundamental mathematical properties, and in particular seeing some mathematical reasoning

Both of these goals are mostly focused on the basic analysis of integrals and derivations, and some famous functions such as trigonometric functions and the exponential function.

• Mathematical Induction
• Completeness
• Functions
• Integral for Step Functions
• Integral for More General Functions
• Applications of Integration
• Limits
• Continuity
• Intermediate Value Theorem
• Inversion
• Extreme - Value Theorem
• Integrability Theorem
• Mean - Value Theorem for Integrals
• Derivatives
• Implicit Differentiation
• Extreme Values
• Mean - Value Theorem for Derivatives
• Curve Sketching
• Fundamental Theorem of Calculus
• Integration by Substitution
• Integration by Parts
• Logarithm
• Exponential Function
• Integration by Partial Fractions
• Complex Numbers