Overview

Embark on a comprehensive 12-hour calculus course covering fundamental concepts from limits to integration. Learn to estimate and solve limits, understand the limit definition, and explore continuity. Master derivatives, including the power rule, chain rule, and implicit differentiation. Dive into applications like related rates and optimization problems. Study antiderivatives, area under curves, and Riemann sums. Explore the Fundamental Theorem of Calculus and various integration techniques. Gain a solid foundation in calculus through detailed explanations, examples, and problem-solving strategies.

Syllabus

Welcome to Calculus 1.
1.1 Introduction to Limits.
1.2 Estimating Limits.
1.3 Limits that Fail to Exist [01] - |x|/x.
1.3 Limit that Fails to Exist [02] - 1/x^2.
1.3 Limits that Fail to Exist [03] - sin(1/x).
1.4 Properties of LImits.
1.5 Solving Limits [01] (Factoring).
1.5 Solving Limits [02] (Rationalization).
1.5 Solving Limits [03] (Fractions).
1.6 Trig Limits [01] (1-cosx/x).
1.6 Trig Limits [02] (tanx/x & sin3x/x).
1.7 Limit Definition - Epsilon Delta [01] (NEW).
1.7 Limit Definition - Epsilon Delta [02].
1.7 Epsilon Delta Limit Definition [03] (example 1).
1.7 Proving a Limit: x^2 = 4 (advanced).
1.8 One Sided Limits.
1.8 One Sided Limit (example 1).
1.8 Continuity.
1.8 Continuity (example 1).
1.6 Trig Limits [03] Proof of sinx/x.
1.9 Geometric Interpretation of sec(x) and tan(x).
1.9 Geometry of [1 - cos(x)/x].
1.9 Problem Solving [01].
1.9 Problem Solving [02].
2.1 - Definition of the Derivative.
2.1 Finding the Slope of a Tangent Line - Example 1.
2.1 Finding the Slope of Tangent Line - Example 2.
2.1 Finding the Slope of a Tangent Line - Example 3.
2.2 Function vs. Derivative - Example 1.
2.2 Function vs. Derivative - Example 2.
2.2 Function vs. Derivative - Example 3.
2.3 Derivative of a Constant.
2.3 Power Rule.
2.4 Derivative of sin(x).
2.4 Derivatives - Trig Functions.
2.5 Product Rule.
2.6 Chain Rule (function notation).
2.6 Chain Rule (Leibniz notation).
2.6 Chain Rule - Example 1 - e^(2x).
2.6 Chain Rule - Example 2 - sin(x^2 + 1).
2.6 Chain Rule - Example 3 - Advanced.
2.7 Quotient Rule 01.
2.7 Quotient Rule 02.
2.8 Introduction to Implicit Differentiation.
2.8 Implicit Differentation (example 1).
2.8 Implicit Differentiation (example 2) - ln(x).
2.8 Derivative of arcsin(x).
2.8 Derivative of arcsec(x).
2.9 Related Rates Introduction.
2.9 Relates Rates Example 01 (Filling a Pool).
2.9 Related Rates Example 02 (Filling a Trough).
2.9 Related Rates Example 03 (Security Laser Part 1).
2.9 Related Rates Example 03 (Security Laser Part 2).
2.9 Related Rates Example 04 (Man walking with his shadow).
3.1 Introduction to Extrema.
3.1 Extrema Example.
3.1 Critical Numbers.
3.2 Finding Critical Numbers [Example 1].
3.2 Finding Critical Numbers [Example 2].
3.2 Finding Critical Numbers [Example 3].
3.2 Finding Critical Numbers [Example 4].
3.2 Finding Critical Numbers [Example 5].
3.3 Rolle's Theorem.
3.3 Mean Value Theorem.
3.3 Mean Value Thereom Example (prove a car was speeding).
3.4 First Derivative Test [Example 1].
3.4 First Derivative Test [Example 2] (Part 1).
3.4 First Derivative Test [Example 2] (Part 2).
3.5 Introduction to Concavity.
3.5 Concavity and the Second Derivative [1].
3.5 Inflection Points.
3.5 Concavity and the Second Derivative [2].
3.6 Optimization - Box with max volume (Part 1).
3.6 Optimization - Box with max volume (Part 2).
3.6 Optimization 02 (circle and square with maximum area).
3.7 Linear Approximation.
4.1 Introduction to Antiderivatives.
4.1 Antiderivative Power Rule.
4.1 Basic Properties of Antiderivatives.
4.1 Common Antiderivatives.
4.2 Intro to Area Under a Curve.
Summation Formulas and Sigma Notation (Part 1) Notation.
Summation Formulas and Sigma Notation (Part 2) Formulas.
Summation Formulas and Sigma Notation (Part 3) Advanced Properties.
Summation Formulas and Sigma Notation (Part 4) Examples.
4.2 Estimating the Area Under a Curve.
4.3 Exact Area Under A Curve.
4.3 Exact Area Under a Curve 02.
4.3 Exact Area - Left Hand Sum.
4.3 Exact Area Under a Curve 3.
4.4 Riemann Sum and the Definite Integral.
4.5 First Fundamental Thereom of Calculus.
4.5 First Fundamental Theorem of Calculus (Examples).
4.6 Properties of Integrals.
4.6 Area Under the x-axis.
4.6 Average Value of a Function.
5.1 Integration: Re-Writing an Integral - Ex.1.
5.1 Integration: Re-Writing an Integral - Ex.2.
5.1 Integration: Re-Writing an Integral - Ex.3.
5.2 Integration: U-Substitution - Ex.1.
5.2 Integration: U-Substitution - Ex.2.
5.2 Integration: U-Substitution - Ex.3.
5.2 Integration | U-Substitution - Ex. 4.
5.2 Integration | U-Substitution - Ex. 5.
5.2 Integration | U-Substitution - Ex.6.
5.3 Integration | Natural Log (ln) - Ex.1.
5.3 Integration | Natural Log (ln) - Ex.2.
5.3 Integration | Natural Log (ln) - Ex.3.
5.3 Integration | Natural Log (ln) - Ex. 4.
5.4 Integration | Integral of secx.
5.4 Integration | Integral of tanx.