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About course

Mathematics course that covers the calculus section especially for the Maths 1 major at the University of the Witwatersrand.

Syllabus

Section 1. Limits and Continuity

What is a Limit? Basic Idea of Limits

Finding Limits From a Graph

Calculating a Limt By Factoring and Canceling

Calculating a Limit by Getting a Common Denominator

Calculating a Limit by Expanding and Simplfiying

Calculating a Limit by Multiplying by a Conjugate

Limits Involving Absolute Value

Calculating a Limit Involving sin(x)/x as x approaches zero

The Squeeze Theorem for Limits, Example 1

Calculus - Infinite Limits

Limits at Infinity - Basic Idea and Shortcuts!

Calculating a Limit at Infinity with a Radical

Continuity - Part 1 of 2

Continuity - Part 2 of 2

Section 2. Differentiation

Understanding the Definition of the Derivative

Sketching the Derivative of a Function

Basic Derivative Examples

The Product Rule for Derivatives

The Quotient Rule

Chain Rule for Finding Derivatives

Finding the Equation of a Tangent Line

Equation of Tangent Line Using Definition of Derivative

Finding the Equation of a Tangent Line Using a Derivative, Ex 2

Basic Chain Rule Problems

Derivatives - Product + Chain Rule + Factoring

Chain Rule + Product Rule + Simplifying - Example 1

Chain Rule + Product Rule + Simplifying - Example 2

Chain Rule +Quotient Rule + Simplifying

Using the Chain Rule - Harder Example #1

Using the Chain Rule - Harder Example #2

Using the Chain Rule - Harder Example #3

More Complicated Derivative Examples

More Complicated Derivative Examples #2

Finding Critical Numbers - Example 1

Finding Critical Numbers - Example 2

Finding Intervals of Increase/Decrease Local Max/Mins

Finding Local Maximums/Minimums - Second Derivative Test

The Mean Value Theorem

Proof By Contradiction - Calculus Based Example

The Closed Interval Method to Find Absolute Maximums and Minimums

Implicit Differentiation - Basic Idea and Examples

Using Implicit Differentiation - Extra Examples

More! Implicit Differentiation Examples

Using Implicit Differentiation to find a Second Derivative

Related Rates #3 - A point on a graph

Related Rates Involving Baseball!

Related Rates Problem Using Implicit Differentiation

Related Rates Involving Trigonometry

Related Rates Using Cones

Curve Sketching Using Calculus - Part 1 of 2

Curve Sketching Using Calculus - Part 2of 2

Summary of Curve Sketching - Example 2, Part 1 of 4

Summary of Curve Sketching - Example 2 - Part 2 of 4

Summary of Curve Sketching - Example 2 - Part 3 of 4

Summary of Curve Sketching - Example 2 - Part 4 of 4

Optimization Problem #1

Optimization Problem #2

Optimization Problem #3 - Making a Rain Gutter

Derivatives of Logarithmic Functions

Derivatives of Logarithmic Functions - More Examples

Logarithmic Differentiation

Logarithmic Differentiation - Example 2

Logarithmic Differentiation - Example 3

Inverse Trigonometric Functions - Derivatives

Inverse Trigonometric Functions - Derivatives - Example 2

Inverse Trigonometric Functions - Derivatives - Example 3

Derivatives of Exponential Functions

Section 3. Integration

The Definite Integral - Understanding the Definition

Approximating a Definite Integral Using Rectangles

Calculating a Definite Integral Using Riemann Sums - Part 1

Calculating a Definite Integral Using Riemann Sums - Part 2

Integration using U-Substitution

Integration by U-Substitution, Definite Integral

U-substitution - Indefinite Integral, Another 2 examples

U-Substitution - More Complicated Examples

Negative Exponents

Integrating Exponential Functions - Examples 1 and 2

Integrating Exponential Functions - Examples 3 and 4

Integration by Parts

Integration by Parts - Definite Integral

Integration By Parts - Using IBP's Twice

Integration by Parts - A Loopy Example!

Trigonometric Integrals - Part 1 of 6

Trigonometric Integrals - Part 2 of 6

Trigonometric Integrals - Part 3 of 6

Trigonometric Integrals - Part 4 of 6

Trigonometric Integrals - Part 5 of 6

Trigonometric Integrals - Part 6 of 6

Trigonometric Substitution - Example 2

Trigonometric Substitution - Example 3 / Part 1

Trigonometric Substitution - Example 3 / Part 2

Integration Using Partial Fractions / Rationalizing Sub

A Complete Partial Fractions Problem

A Complete Partial Fractions Problem

Determining Coefficients for Partial Fractions

Partial Fraction Decompositions and Long Division

Finding Areas Between Curves

Fundamental Theorem of Calculus Part 1

Area Between Curves - Integrating with Respect to y

Area Between Curves - Integrating with Respect to y - Part 2

Volumes of Revolution about Vertical Lines Using Washers

Volumes of Revolution - Disk/Washers Example 1

Volumes of Revolution - Disk/Washers Example 2

Volumes of Revolution - Cylindrical Shells

Volumes of Revolution - Disk/Washers Example 3

Longer Version - Volumes using Cylindrical Shells

Hyperbolic Functions - The Basics

Hyperbolic Functions - Derivatives

Inverse Hyperbolic Functions - Derivatives

Section 4. L'Hopitals Rule and Improper Integrals

Section 5. Sequence and Series

What is a Sequence? Basic Sequence Info

Recursive Sequences

Arithmetic Sequences: Finding a General Formula Given Two Terms

Quick Intro to Arithmetic Sequences

A Quick Intro to Geometric Sequences

Geometric Sequences: A Formula for the' n - th ' Term.

Sequences - Examples showing convergence or divergence

Summation Notation

What is a Series

Finding the Sum of a Finite Arithmetic Series

Geometric Series - Expressing a Decimal as a Rational Number

Showing a Series Diverges using Partial Sums

Geometric Series and the Test for Divergence - Part 1

Geometric Series and the Test for Divergence - Part 2

Telescoping Series Example

Limit Comparison Test and Direct Comparison Test Part 2

Using the Integral Test for Series

Limit Comparison Test and Direct Comparison Test

Remainder Estimate for the Integral Test

Alternating Series

More Alternating Series Examples

Alternating Series Estimation Theorem

Using the Ratio Test to Determine if a Series Converges #1

Using the Ratio Test to Determine if a Series Converges #2

Absolute Convergence, Conditional Convergence and Divergence

Strategy for Testing Series - Series Practice Problems

Power Series - Finding the Interval of Convergence

Radius of Convergence for a Power Series

Power Series Representation of Functions

Differentiating and Integrating Power Series

Multiplication and Division of Power Series

Taylor and Maclaurin Series - Example 1

Taylor and Maclaurin Series - Example 2

Taylor / Maclaurin Series for Sin (x)

Using Series to Evaluate Limits

Using Maclaurin/Taylor Series to Approximate a Definite Integral to a Desired Accuracy

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