Calculus

Calculus, developed by Newton and Leibniz, is the branch of mathematics that helps us study how quantities change and how they accumulate. It allows us to understand motion, growth rates and areas under curves.

Calculus has two main parts:

1. Differential Calculus: study of derivatives and rates of change
2. Integral Calculus: study of accumulation, areas and total values

Calculus 1: Limits, Continuity, and Differentiation

Build a strong foundation in limits, derivatives and the fundamental concepts of calculus.

Limits and Continuity

• Graphs and Limits
• Definition of a Limit
• One-Sided Limits
• Limit Laws
• Limits of Piecewise Functions
• Squeeze Theorem
• Limits and Continuity
• Limits at Infinity
• Intermediate Value Theorem

Derivatives Basics

• Average Rate of Change
• Limit Definition of Derivative
• Tangent Line Equations
• Differentiability
• Power Rule
• Product Rule
• Quotient Rule

Special Derivatives

• Derivatives of Trigonometric Functions
• Chain Rule
• Derivatives of Exponential Functions
• Derivatives of Logarithmic Functions
• Logarithmic Differentiation
• Derivatives of Inverse Trigonometric Functions

Applications of Derivatives

• Maxima and Minima
• First & Second Derivative Tests
• Extreme Value Examples
• Mean Value Theorem (and Proof)
• Concavity
• Curve Sketching
• Higher Order Derivatives
• Linear Approximation and Differentials
• L'Hôpital's Rule
• Indeterminate forms
• Newton's Method
• Real-Life Applications

Introduction to Integration

• Antiderivatives
• Summation Notation
• Riemann Sums
• Fundamental Theorem of Calculus (Parts 1 & 2)

Calculus II: Integration, Series, and Advanced Topics

Explore advanced integration techniques, infinite series and multivariable concepts.

Integration Techniques

• Substitution
• Integration by Parts
• Trigonometric Integrals
• Trigonometric Substitution
• Partial Fractions
• Improper Integrals

Applications of Integration

• Area Between Curves
• Volumes (Disks and Washers)
• Arc Length
• Surface Area of Revolution

Sequences and Series

• Sequences (Limits of Sequences)
• Convergence Tests
• Power Series
• Taylor and Maclaurin Series

Advanced Calculus Topics

• Parametric Equations
• Basic Differential Equations
• Separable Equations

Practice for Calculus

Strengthen your understanding of calculus concepts through quizzes and practice problems.

• Limits Quiz
• Continuity of Function Quiz
• Maxima and Minima Quiz
• Integration Quiz
• Practice Questions on Calculus

Programs for Calculus

Apply calculus concepts using programming tools such as Python and MATLAB.

• Calculus with Python
• Program to Differentiate Given Polynomial
• Program to Calculate Double Integration
• Calculus in MATLAB