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Tutoring Centers: Mathematics Resources: MAC 2311: Calculus I w/ Analytic Geometry

MAC 2311: Calculus I with Analytic Geometry

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MAC 2311: Calculus I with Analytic Geometry examines major topics that include limits, differentiation of algebraic, exponential, logarithmic, and trigonometric functions; and applications of derivatives. The student explores the definite and indefinite integral and investigates their applications. This course is for students who need calculus for engineering, math, and science programs.

Test 1: Limits

Graphical Limits

What is a Limit?

DNE Limits

Limits from the Graph

Intro to Graphical Limits; Part 1

Intro to Graphical Limits; Part 2

Sketching a Graph, Given Limits

Numerical Limits

What is a Limit?

DNE Limits

Approximating Limits

Numerical Limits; Part 1

Numerical Limits; Part 2

Analytic Limits

What is a Limit?

Limit of a Constant

Limits & Factoring

Limits & Rational Functions

Special Limits

Trigonometric Limits

Intro to Analytic Limits

Limits Examples; Part 1

Limit Examples; Part 2

Limits Involving Infinity

What is a Limit?

DNE Limits

Removeable vs Nonremovable Discontinuities

Holes vs Horizontal Asymptotes

Intro to Limits at Infinity

Limits at Infinity

Continuity

What is a Limit?

DNE Limits

Introduction to Continuity

Limits and Continuity

Test 2: Derivatives

The Limit Definitions of the Derivative

What is a Derivative?

The Limit Definition

The Alt Limit Definition

Limit Def. of the Derivative

Using the Limit Def.-

Alternate Limit Def.-

Basic Rules of Differentiation

Power Rule; Part 1

Power Rule; Part 2

Equation of Tangent Line

The Product and Quotient Rules

The Product Rule

The Quotient Rule

Horizontal/Vertical Tangencies

Derivatives of Trigonometric Functions

Derivatives of the 6 functions

Remembering the Trig Derivatives

Derivatives of Logarithmic and Exponential Functions

Logarithmic Differentiation; Part 1

Logarithmic Differentiation; Part 2

Logarithmic Differentiation; Part 3

Higher Order Derivatives

Higher Order Derivatives; Part 1

Higher Order Derivatives; Part 2

Higher Order Derivatives/Applications

The Derivative as a Rate of Change

Intro to Derivatives as a ROC

Example 1

Example 2

The Chain Rule

Intro to the Chain Rule

When to Use the Chain Rule

The Chain Rule, continued

Implicit Differentiation

Implicit Differentiation; Part 1

Implicit Differentiation; Part 2

Example

Logarithmic Differentiation

Logarithmic Differentiation; Part 1

Logarithmic Differentiation; Part 2

Logarithmic Differentiation; Part 3

Derivatives of Inverse Functions

Derivatives of Inverse Functions; Part 1

Derivatives of Inverse Functions; Part 2

Derivatives of Inverse Trig Functions

Related Rates

How to Solve Related Rates Problems

Example: The Ladder Problem

Example: The Shadow Problem

Test 3: Applications of the Derivative

Critical Values

Intro to Critical Values

Critical Points on a Graph

Example

Extrema on a Closed Interval

Relative Extrema

Absolute Extrema

Extrema on a Closed Interval

Rolle's Theorem and the Mean Value Theorem

Rolle’s Theorem and the MVT

Rolle’s Theorem

MVT

Analysis of the First Derivative

First Derivative Test; Part 1

First Derivative Test; Part 2

Example

Analysis of the Second Derivative

Graph Analysis

Second Derivative Test

Concavity and Inflection

L'Hopital's Rule

L’Hopital’s Rule; Part 1

L’Hopital’s Rule; Part 2

L’Hopital’s Rule; Part 3

Curve Sketching

Curve Sketching; Part 1

Curve Sketching; Part 2

Curve Sketching; Part 3

Optimization Applications

Optimization; Part 1

Optimization; Part 2

Optimization; Part 3

Integrals

An Introduction to Antidifferentiation

Intro to Antidifferentiation

Basic examples

More examples

Antidifferentiation via Substitution

Integration by Substitution; Part 1

Integration by Substitution; Part 2

Integration by Substitution; Part 3

An Introduction to Differential Equations

Separation of Variables

Differential Equation Practice

Review of Differential Equations

A Geometric Introduction to the Definite Integral

Evaluating Integrals with Geometry

Geometric Approach to Integrals; Part 1

Geometric Approach to Integrals; Part 2

The Limit Definition and Properties of the Definite Integral

Name

The Second Fundamental Theorem of Calculus

How to use 2nd FTC

Example

More With the 2nd FTC

The Mean Value Theorem for Definite Integrals

MVT for Definite Integrals; Part 1

MVT for Definite Integrals; Part 2

The First Fundamental Theorem of Calculus

The 1st FTC; Part 1

The 1st FTC; Part 2

The 1st FTC; Part 3

Test Reviews

Recorded Review Lectures for MAC 2311

Useful Links

Math Department Simple Syllabus

IRSC Mathematics Faculty

Mathematics Programs

Careers in Mathematics & Engineering

IRSC STEM Pioneer Grant

Tools for Overcoming Test Anxiety

Acknowledgments

This MAC 2311 course guide would not have been possible without Josh Caron and Victoria Dearman.