MTH5101 — Calculus 1

Lectures (150)

Welcome to Calculus-1: Course Welcome and Introduction | Calculus 1 | MTH5101_Topic001

Review of Sets | Calculus 1 | MTH5101_Topic002

Real Numbers | Calculus 1 | MTH5101_Topic003

Exponents and Scientific Notation | Calculus 1 | MTH5101_Topic004

Radicals and Rational Exponents | Calculus 1 | MTH5101_Topic005

Polynomials | Calculus 1 | MTH5101_Topic006

Factoring of a Polynomial | Calculus 1 | MTH5101_Topic007

Rational Expressions | Calculus 1 | MTH5101_Topic008

Foundations of the Cartesian Plane and Plotting Points | Calculus 1 | MTH5101_Topic009

Graphing with Intercepts, Distance, and Midpoint Techniques | Calculus 1 | MTH5101_Topic010

Solving Linear and Quadratic Equations | Calculus 1 | MTH5101_Topic011

Absolute Value Equations & Basic Inequalities | Calculus 1 | MTH5101_Topic012

Absolute Value Inequalities | Calculus 1 | MTH5101_Topic013

Function Definition and Notation | Calculus 1 | MTH5101_Topic014

Domain and Range | Calculus 1 | MTH5101_Topic015

Graphing Functions and Zeros | Calculus 1 | MTH5101_Topic016

Combining Functions and Symmetry | Calculus 1 | MTH5101_Topic017

Linear Functions and Slope | Calculus 1 | MTH5101_Topic018

Polynomial Functions and Degree | Calculus 1 | MTH5101_Topic019

Quadratic Functions and Roots | Calculus 1 | MTH5101_Topic020

Rational Functions | Calculus 1 | MTH5101_Topic021

Power and Root Functions | Calculus 1 | MTH5101_Topic022

Algebraic vs Transcendental Functions | Calculus 1 | MTH5101_Topic023

Piecewise-Defined Functions and Graphs | Calculus 1 | MTH5101_Topic024

Angle Measure and Radians | Calculus 1 | MTH5101_Topic025

Trigonometric Functions | Calculus 1 | MTH5101_Topic026

Trigonometric Identities | Calculus 1 | MTH5101_Topic027

Graphs and Periods of Trigonometric Functions | Calculus 1 | MTH5101_Topic028

Inverse Functions | Calculus 1 | MTH5101_Topic029

Finding Inverses, Graphing Inverses, and Restricted Domains | Calculus 1 | MTH5101_Topic030

Inverse Trigonometric Functions | Calculus 1 | MTH5101_Topic031

Exponential Functions | Calculus 1 | MTH5101_Topic032

Laws of Exponents, and the Number e | Calculus 1 | MTH5101_Topic033

Logarithmic Functions | Calculus 1 | MTH5101_Topic034

Equations and Applications Involving Logarithms | Calculus 1 | MTH5101_Topic035

Hyperbolic Functions | Calculus 1 | MTH5101_Topic036

The Tangent Problem | Calculus 1 | MTH5101_Topic037

Instantaneous Velocity and the Limit Process | Calculus 1 | MTH5101_Topic038

What a Limit Means and Proper Notation | Calculus 1 | MTH5101_Topic039

Estimating Limits Using Tables | Calculus 1 | MTH5101_Topic040

Estimating Limits from Graphs and When Limits Fail | Calculus 1 | MTH5101_Topic041

One-Sided Limits and their Relationship to Two-Sided Limits | Calculus 1 | MTH5101_Topic042

Infinite Limits and Vertical Asymptotes | Calculus 1 | MTH5101_Topic043

Basic Limit Laws | Calculus 1 | MTH5101_Topic044

Applying the Limit Laws | Calculus 1 | MTH5101_Topic045

Polynomial and Rational Function Limits | Calculus 1 | MTH5101_Topic046

Factoring and Conjugate Techniques | Calculus 1 | MTH5101_Topic047

Indeterminate (0/0) Form: Factor and Cancel | Calculus 1 | MTH5101_Topic048

Conjugates for Radical Expressions | Calculus 1 | MTH5101_Topic049

Simplifying Complex Fractions and Creative Algebra | Calculus 1 | MTH5101_Topic050

Evaluating Two Sided Limits Algebraically | Calculus 1 | MTH5101_Topic051

Limits of the Form K/0 and Infinite Behavior | Calculus 1 | MTH5101_Topic052

Fundamental Trigonometric Limits and the Squeeze Theorem | Calculus 1 | MTH5101_Topic053

Continuity at a Point: The Three Conditions | Calculus 1 | MTH5101_Topic054

Types of Discontinuities and Intermediate Value Theorem | Calculus 1 | MTH5101_Topic055

Solving for K to Ensure Continuity at x=a | Calculus 1 | MTH5101_Topic056

Review of Limits & Continuity | Calculus 1 | MTH5101_Topic057

Tangent Lines and Secant Lines | Calculus 1 | MTH5101_Topic058

The Derivative as a Limit | Calculus 1 | MTH5101_Topic059

Estimating and Calculating Derivatives | Calculus 1 | MTH5101_Topic060

Velocity and Instantaneous Rate of Change | Calculus 1 | MTH5101_Topic061

Defining the Derivative Function | Calculus 1 | MTH5101_Topic062

Graphing Derivatives and Differentiability | Calculus 1 | MTH5101_Topic063

Higher Order Derivatives | Calculus 1 | MTH5101_Topic064

The Constant Rule | Calculus 1 | MTH5101_Topic065

The Power Rule (Positive Integers) | Calculus 1 | MTH5101_Topic066

Power Rule for Negative Exponents | Calculus 1 | MTH5101_Topic067

The Constant Multiple Rule | Calculus 1 | MTH5101_Topic068

The Sum and Difference Rules | Calculus 1 | MTH5101_Topic069

Combining Rules for Polynomials and Tangent Lines | Calculus 1 | MTH5101_Topic070

The Product Rule | Calculus 1 | MTH5101_Topic071

Applying the Product Rule | Calculus 1 | MTH5101_Topic072

The Quotient Rule | Calculus 1 | MTH5101_Topic073

Combining Differentiation Rules | Calculus 1 | MTH5101_Topic074

Equations of Tangent Line | Calculus 1 | MTH5101_Topic075

Derivatives of sin x and cos x | Calculus 1 | MTH5101_Topic076

Derivatives of tan x, cot x, sec x and cosec x | Calculus 1 | MTH5101_Topic077

The Chain Rule | Calculus 1 | MTH5101_Topic078

Chain Rule with Power Rule and Trigonometric Functions | Calculus 1 | MTH5101_Topic079

Advanced Chain Rule Applications | Calculus 1 | MTH5101_Topic080

Derivatives of Exponential Functions | Calculus 1 | MTH5101_Topic081

Derivatives of Logarithmic Functions | Calculus 1 | MTH5101_Topic082

Implicit Differentiation | Calculus 1 | MTH5101_Topic083

Derivative of Inverse Trigonometric Functions | Calculus 1 | MTH5101_Topic084

Equations of Tangent Line | Calculus 1 | MTH5101_Topic085

Higher-order Derivatives Using Differentiation Rules | Calculus 1 | MTH5101_Topic086

Amount of Change, and Average vs Instantaneous Rates | Calculus 1 | MTH5101_Topic087

Application of Rate of Change: Motion Along a Line | Calculus 1 | MTH5101_Topic088

Linear Approximations | Calculus 1 | MTH5101_Topic089

Differentials and Error Analysis | Calculus 1 | MTH5101_Topic090

Absolute Extrema and the Extreme Value Theorem | Calculus 1 | MTH5101_Topic091

Local Extrema, Critical Numbers and Fermat’s Theorem | Calculus 1 | MTH5101_Topic092

Systematic Search for Critical Points | Calculus 1 | MTH5101_Topic093

Locating Absolute Extrema on Closed Intervals | Calculus 1 | MTH5101_Topic094

Increasing/Decreasing via the First Derivative | Calculus 1 | MTH5101_Topic095

The First Derivative Test (Classifying Critical Points) | Calculus 1 | MTH5101_Topic096

Mean Value Theorem (Rolle's Theorem → MVT) | Calculus 1 | MTH5101_Topic097

MVT Consequences, Inequalities & Velocity | Calculus 1 | MTH5101_Topic098

Concavity, and Point of Inflection (1) | Calculus 1 | MTH5101_Topic099

Concavity, and Point of Inflection (2) | Calculus 1 | MTH5101_Topic100

The Second Derivative Test (1) | Calculus 1 | MTH5101_Topic101

The Second Derivative Test (2) | Calculus 1 | MTH5101_Topic102

Determining Monotonicity and Extrema from Graphs | Calculus 1 | MTH5101_Topic103

Applied Optimization (1) – Closed Intervals | Calculus 1 | MTH5101_Topic104

Applied Optimization (2) - Closed Intervals | Calculus 1 | MTH5101_Topic105

Related Rates | Calculus 1 | MTH5101_Topic106

Limits at Infinity | Calculus 1 | MTH5101_Topic107

End Behaviour of Functions | Calculus 1 | MTH5101_Topic108

Graphing a Function Using Limits and Derivatives (1) | Calculus 1 | MTH5101_Topic109

Graphing a Function Using Limits and Derivatives (2) | Calculus 1 | MTH5101_Topic110

L’Hôpital’s Rule: When and How to Use | Calculus 1 | MTH5101_Topic111

L’Hôpital’s Rule: Other Indeterminate Forms and the Log Trick | Calculus 1 | MTH5101_Topic112

Introduction to Antiderivatives and Indefinite Integrals | Calculus 1 | MTH5101_Topic113

Properties of Integrals and Initial-value Problems | Calculus 1 | MTH5101_Topic114

Sigma (Summation) Notation: The Language of Long Sums | Calculus 1 | MTH5101_Topic115

From Sums to Areas: Rectangular Approximations | Calculus 1 | MTH5101_Topic116

Riemann Sums: Leading to the Exact Area | Calculus 1 | MTH5101_Topic117

The Definite Integral: Definition, Notation, and Meaning | Calculus 1 | MTH5101_Topic118

Building Riemann Sums, and Evaluating by Definition | Calculus 1 | MTH5101_Topic119

Evaluating by Geometry (Exact Areas from Simple Shapes) | Calculus 1 | MTH5101_Topic120

Evaluating Net Signed Area by Geometry | Calculus 1 | MTH5101_Topic121

Evaluating Total Area by Geometry | Calculus 1 | MTH5101_Topic122

Properties of the Definite Integral | Calculus 1 | MTH5101_Topic123

Comparison Properties of Integrals | Calculus 1 | MTH5101_Topic124

Average Value of a Function, and Mean Value Theorem for Integrals | Calculus 1 | MTH5101_Topic125

Fundamental Theorem of Calculus Part I (Integrals & Antiderivatives) | Calculus 1 | MTH5101_Topic126

Fundamental Theorem of Calculus Part I (Two Variable Limits of Integration) | MTH5101_Topic127

Fundamental Theorem of Calculus Part II (Evaluation Theorem) | Calculus 1 | MTH5101_Topic128

Evaluating Integrals by Formulas (Algebraic Functions) | Calculus 1 | MTH5101_Topic129

Evaluating Integrals by Formulas (Transcendental Functions) | Calculus 1 | MTH5101_Topic130

The Net Change Theorem | Calculus 1 | MTH5101_Topic131

Applying the Net Change Theorem | Calculus 1 | MTH5101_Topic132

Integrals of Even and Odd Functions with Symmetric Limits | Calculus 1 | MTH5101_Topic133

Substitution Rule for Indefinite Integrals: Algebraic Functions | Calculus 1 | MTH5101_Topic134

Substitution Rule for Indefinite Integrals: Transcendental Functions | Calculus 1 | MTH5101_Topic135

Substitution Rule for Definite Integrals | Calculus 1 | MTH5101_Topic136

Substitution Rule Strategy and Common Patterns | Calculus 1 | MTH5101_Topic137

Integrals of Exponential Functions | Calculus 1 | MTH5101_Topic138

Integrals of Exponential Functions Real-life Applications | Calculus 1 | MTH5101_Topic139

Integrals of Logarithmic Functions | Calculus 1 | MTH5101_Topic140

Integration by Parts | Calculus 1 | MTH5101_Topic141

Applying Integration by Parts More Than Once | Calculus 1 | MTH5101_Topic142

Integration by Parts for Definite Integrals | Calculus 1 | MTH5101_Topic143

Area between Two Curves - (I) | Calculus 1 | MTH5101_Topic144

Area between Two Curves - (II) | Calculus 1 | MTH5101_Topic145

Areas for Intersections and Compound Regions | Calculus 1 | MTH5101_Topic146

Arc Length of a Curve | Calculus 1 | MTH5101_Topic147

Physical Applications: Mass and Density | Calculus 1 | MTH5101_Topic148

Physical Applications: Work Done by a Force | Calculus 1 | MTH5101_Topic149

Physical Applications: Springs and Hooke’s Law | Calculus 1 | MTH5101_Topic150