The following video provides an outline of all the topics you would expect to see in a typical **Single-Variable Calculus 1** class (i.e., Calculus 1, Business Calculus 1, AB Calculus, BC Calculus, or IB HL 2 Mathematics).

All of the topics are covered in detail in our Online Calculus 1 Course. The course contains full lectures, detailed examples, and also includes practice final exams.

## Calculus 1 Syllabus

Calculus 1 Overview

The following sections provide links to our complete lessons on all Calculus 1 topics.

Also, be sure to check out our FREE calculus tutoring videos and read our reviews to see what we’re like.

## Limits

- Finding limits graphically, numerically and algebraically

– one sided limits

– two sided limits

– limits going to infinity - Finding limits of indeterminate forms

– Factoring, common denominators, and conjugate manipulations

– Trig manipulations - Limit Definition of Derivative and Continuity

– Finding basic derivatives using the limit definition of derivative

– Writing equations of tangent lines and normal lines

– Proving a function is continuous or discontinuous

## Derivatives

- Derivative Rules Part 1

– Power Rule

– Product Rule

– Quotient Rule

– Chain Rule

– Exponential and Logarithmic Rules

– Trigonometric and Arc Function Rules - Derivative Rules Part 2

– Combination of Rules and Simplifying Derivatives

– Writing equations of tangent lines and normal lines using derivative rules

– Average Rate of Change vs. Instantaneous rate of change

## Application of Derivatives

- Extrema and Curve Sketching

– First Derivative Test – Finding critical numbers, maximums, minimums, increasing intervals, and decreasing intervals

– Second Derivative Test – Finding inflection points and concavity - Theorems

– Average Rate of Change

– Mean Value Theorem

– Rolle’s Theorem

– Differentiability - Particle Motion

– Position, velocity, and accelerations

– Discovering when an object is at rest and when an object changes direction.

– Distance vs. Total distance traveled - Graphing Derivatives and proving continuity and differentiability

## Integrals

- Riemann Sums and Trapezoidal Sums to calculate area under a curve
- Integration Rules for all functions using Indefinite Integrals
- Fundamental Theorem of Calculus 1 and 2

– FTC#1 – definite integrals

– FTC#2 – derivative of an integral - Integration using Partial Fractions, Integration by Parts, and Improper Integrals

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