MTH5102 — Calculus II

Lectures (176)

Introduction: What this Course is About? | Calculus II | MTH5102_Topic001

Explain Sigma Notation and its Properties | Calculus II | MTH5102_Topic002

Rule, Sums and Powers of Integers | Calculus II | MTH5102_Topic003

Approximating the Area Under a Curve | Calculus II | MTH5102_Topic004

Define Riemann Sums | Calculus II | MTH5102_Topic005

Define Definite Integral | Calculus II | MTH5102_Topic006

Geometric Formulas to Calculate Definite Integrals | Calculus II | MTH5102_Topic007

Net Signed Area | Calculus II | MTH5102_Topic008

Finding the Total Area | Calculus II | MTH5102_Topic009

Properties of the Definite Integral | Calculus II | MTH5102_Topic010

The Mean Value Theorem for Definite Integrals | Calculus II | MTH5102_Topic011

Fundamental Theorem of Calculus: FTC - (Part-1) | Calculus II | MTH5102_Topic012

Example of FTC - (Part-1) | Calculus II | MTH5102_Topic013

Fundamental Theorem of Calculus: FTC - (Part-2) | Calculus II | MTH5102_Topic014

Application of FTC | Calculus II | MTH5102_Topic015

Substitution with Indefinite Integrals: Part-1 | Calculus II | MTH5102_Topic016

Substitution with Indefinite Integrals: Part-2 | Calculus II | MTH5102_Topic017

Substitution for Definite Integrals | Calculus II | MTH5102_Topic018

Integrals of Exponential Functions (Part 1) | Calculus II | MTH5102_Topic019

Integrals of Exponential Functions (Part 2) | Calculus II | MTH5102_Topic020

Real-Life Applications | Calculus II | MTH5102_Topic021

Integrals Involving Logarithmic Functions | Calculus II | MTH5102_Topic022

Finding Antiderivative Involving an Inverse Trigonometric Function | Calculus II | MTH5102_Topic023

Evaluating a Definite Integral Using Inverse Trigonometric Functions |Calculus II | MTH5102_Topic024

Finding an Antiderivative Involving the Inverse Tangent Function | Calculus II | MTH5102_Topic025

Finding the Area Between Two Curves (Part 1) | Calculus II | MTH5102_Topic026

Finding the Area Between Two Curves (Part 2) | Calculus II | MTH5102_Topic027

Finding the Area Between Two Curves Integrating Along the Y-Exis | Calculus II | MTH5102_Topic028

Finding Volumes by the Slicing Method | Calculus II | MTH5102_Topic029

Deriving the Formula for the Volume of a Pyramid | Calculus II | MTH5102_Topic030

Using Slicing Method to Find the Volume of a Solid of Revolution | Calculus II | MTH5102_Topic031

The Disk Method | Calculus 2 | MTH5102_Topic032

The Disk Method Around Y-Axis | Calculus II | MTH5102_Topic033

The Washer Method | Calculus II | MTH5102_Topic034

The Washer Method Around Y-Axis | Calculus II | MTH5102_Topic035

Application; Design Water Tank Volumes | Calculus II | MTH5102_Topic036

The Method of Cylindrical Shells | Calculus II | MTH5102_Topic037

The Method of Cylindrical Shells Around Y-Axis and A Line | Calculus II | MTH5102_Topic038

Which Method Should We Use? | Calculus II | MTH5102_Topic039

ARC Length of the Curve | Calculus II | MTH5102_Topic040

Arc Length of the Curve, X=G(Y) | Calculus II | MTH5102_Topic041

Surface Area of a Surface of Revolution | Calculus II | MTH5102_Topic042

Mass-Density Formula of a One-Dimensional Object (Linear Case) | Calculus II | MTH5102_Topic043

Work Done by a Force - (1) | Calculus II | MTH5102_Topic044

Work Done by a Force - (2) | Calculus II | MTH5102_Topic045

Center of Mass of Objects on a Line | Calculus II | MTH5102_Topic046

Center of Mass of Objects in a Plane | Calculus II | MTH5102_Topic047

Center of Mass of a Thin Plate (Part 1) | Calculus II | MTH5102_Topic048

Center of Mass of a Thin Plate (Part 2) | Calculus II | MTH5102_Topic049

Center of Mass of a Lamina Bounded by Two Functions (Part 1) | Calculus II | MTH5102_Topic050

Center of Mass of a Lamina Bounded by Two Functions (Part 2) | Calculus II | MTH5102_Topic051

The Natural Logarithm as an Integral (Part 1) | Calculus II | MTH5102_Topic052

The Natural Logarithm as an Integral (Part 2) | Calculus II | MTH5102_Topic053

Properties of the Natural Logarithm | Calculus II | MTH5102_Topic054

The Exponential Function | Calculus II | MTH5102_Topic055

Properties of the Exponential Function | Calculus II | MTH5102_Topic056

General Logarithmic and Exponential Functions (Part 1) | Calculus II | MTH5102_Topic057

General Logarithmic and Exponential Functions (Part 2) | Calculus II | MTH5102_Topic058

Exponential Growth Model (Part 1) | Calculus II | MTH5102_Topic059

Exponential Growth Model (Part 2) | Calculus II | MTH5102_Topic060

Exponential Growth Model (Part 3) | Calculus II | MTH5102_Topic061

Exponential Decay Model (Part 1) | Calculus II | MTH5102_Topic062

Exponential Decay Model (Part 2) | Calculus II | MTH5102_Topic063

Derivatives and Integrals of the Hyperbolic Functions | Calculus II | MTH5102_Topic064

Integrals Involving Hyperbolic Functions | Calculus II | MTH5102_Topic065

Differentiating Inverse Hyperbolic Functions | Calculus II | MTH5102_Topic066

Integrals Involving Inverse Hyperbolic Functions | Calculus II | MTH5102_Topic067

Using a Catenary to Find the Length of a Cable | Calculus II | MTH5102_Topic068

Deriving the Integration by Parts Formula | Calculus II | MTH5102_Topic069

Using Integration by Parts - (1) | Calculus II | MTH5102_Topic070

Using Integration by Parts - (2) | Calculus II | MTH5102_Topic071

Integration by Parts for Definite Integrals (Part 1) | Calculus II | MTH5102_Topic072

Integration by Parts for Definite Integrals | Calculus II | MTH5102_Topic073

Integrating Products and Powers of sinx and cosx | Calculus II | MTH5102_Topic074

Integrating Even Powers of Sine and Cosine Using Power Reducing Identities | MTH5102_Topic075

Integrating Products and Powers of sinx and cosx, (Part 1) | Calculus II | MTH5102_Topic076

Integrating Products and Powers of tanx and secx, (Part 1) | Calculus II | MTH5102_Topic077

Integrating Products and Powers of sinx and cosx, (Part 2) | Calculus II | MTH5102_Topic078

Integrating Products and Powers of tanx and secx, (Part 2) | Calculus II | MTH5102_Topic079

Reduction Formulas | Calculus II | MTH5102_Topic080

Trigonometric Substitution for Radical Integrals | Calculus II | MTH5102_Topic081

Returning to x-Form After Trigonometric Substitution | Calculus II | MTH5102_Topic082

Integrating Expressions Involving (a+x) | Calculus II | MTH5102_Topic083

Integrating Expressions Involving (x-a) | Calculus II | MTH5102_Topic084

Methods of Partial Fractions | Calculus II | MTH5102_Topic085

No Repeated Linear Factor | Calculus II | MTH5102_Topic086

Repeated Linear Factor | Calculus II | MTH5102_Topic087

Integrating Rational Functions with Irreducible Quadratic Factors | Calculus II | MTH5102_Topic088

Simple Quadratic Factors | Calculus II | MTH5102_Topic089

Numerical Integration and Error Estimation - The Midpoint Rule | Calculus II | MTH5102_Topic090

The Trapezoidal Rule | Calculus II | MTH5102_Topic091

The Trapezoidal Rule: Examples | Calculus II | MTH5102_Topic092

Absolute and Relative Error | Calculus II | MTH5102_Topic093

Error Bounds for the Midpoint and Trapezoidal Rules | Calculus II | MTH5102_Topic094

Simpson's Rule | Calculus II | MTH5102_Topic095

Simpson's Rule: Examples | Calculus II | MTH5102_Topic096

Integrating Over an Infinite Interval | Calculus II | MTH5102_Topic097

Integrating Over An Infinite Interval: Examples | Calculus II | MTH5102_Topic098

Integrating Over an Infinite Interval Examples | Calculus II | MTH5102_Topic099

Integrating Discontinuous Integrand | Calculus II | MTH5102_Topic100

Integrating Over and Indefinite Interval: Examples | Calculus II | MTH5102_Topic101

Fundamental Terminology of Sequences | Calculus II | MTH5102_Topic102

Types of Sequences: Arithmetic and Geometric Sequences | Calculus II | MTH5102_Topic103

Limit of a Sequence | Calculus II | MTH5102_Topic104

Determining Convergence & Finding Limits | Calculus II | MTH5102_Topic105

Squeeze Theorem for Sequences | Calculus II | MTH5102_Topic106

Bounded Sequences | Calculus II | MTH5102_Topic107

Sums and Series | Calculus II | MTH5102_Topic108

Evaluating Limits of Sequences of Partial Sums | Calculus II | MTH5102_Topic109

The Harmonic Series and its Convergence | Calculus II | MTH5102_Topic110

Algebraic Properties of Convergent Series | Calculus II | MTH5102_Topic111

Geometric Series | Calculus II | MTH5102_Topic112

Determining Convergence or Divergence of a Geometric Series | Calculus II | MTH5102_Topic113

Using the Divergence Test | Calculus II | MTH5102_Topic114

Integral Test | Calculus II | MTH5102_Topic115

Using the Integral Test | Calculus II | MTH5102_Topic116

The p-Series and its Convergence | Calculus II | MTH5102_Topic117

Comparison Test | Calculus II | MTH5102_Topic118

Limit Comparison Test (Part 1) | Calculus II | MTH5102_Topic119

Limit Comparison Test (Part 2) | Calculus II | MTH5102_Topic120

The Alternating Series and Convergence | Calculus II | MTH5102_Topic121

The Alternating Series and Convergence | Calculus II | MTH5102_Topic122

Absolute and Conditional Convergence | Calculus II | MTH5102_Topic123

Difference Between Absolute and Conditional Convergence | MTH5102 Calculus II | MTH5102_Topic124

The Ratio Test | MTH5102 Calculus II | MTH5102_Topic125

The Root Test | MTH5102 Calculus II | MTH5102_Topic126

How to Choose the Right Convergence Test? | MTH5102 Calculus II | MTH5102_Topic127

Introduction to Power Series | MTH5102 Calculus II | MTH5102_Topic128

Convergence of a Power Series | MTH5102 Calculus II | MTH5102_Topic129

Convergence of a Power Series Examples | MTH5102 Calculus II | MTH5102_Topic130

Representing Functions Using Power Series (Part 1) | MTH5102 Calculus II | MTH5102_Topic131

Representing Functions as Power Series | Calculus II | MTH5102_Topic132

Differentiating and Integrating Power Series | MTH5102 Calculus II | MTH5102_Topic133

Differentiating and Integrating Power Series Examples (1) | MTH5102 Calculus II | MTH5102_Topic134

Differentiating and Integrating Power Series Examples (2) | MTH5102 Calculus II | MTH5102_Topic135

The Lottery Problem | MTH5102 Calculus II | MTH5102_Topic136

Taylor and Maclaurin Series | MTH5102 Calculus II | MTH5102_Topic137

Examples of Taylor Series | Calculus II | MTH5102_Topic138

Understanding Taylor and Maclaurin Polynomials | MTH5102 Calculus II | MTH5102_Topic139

Finding Maclaurin Polynomials, Examples | MTH5102 Calculus II | MTH5102_Topic140

Understanding Taylor's Theorem and the Remainder Term | MTH5102 Calculus II | MTH5102_Topic141

Estimate Function Values | MTH5102 Calculus II | MTH5102_Topic142

Understanding When Taylor Series Converges to its Function | MTH5102 Calculus II | MTH5102_Topic143

Understanding Parametric Equations | MTH5102 Calculus II | MTH5102_Topic144

Graphing a Parametrically Defined Curve, Examples | MTH5102 Calculus II | MTH5102_Topic145

Parameterizing a Curve, Examples | MTH5102 Calculus II | MTH5102_Topic146

Derivatives of Parametric Equations | MTH5102 Calculus II | MTH5102_Topic147

Finding Slopes and Tangent Lines for Parametric Curves | MTH5102 Calculus II | MTH5102_Topic148

Second-Order Derivatives of Parametric Curves | MTH5102 Calculus II | MTH5102_Topic149

Area Under a Curve Defined by Parametric Equations | MTH5102 Calculus II | MTH5102_Topic150

Finding the Area Under a Parametric Curve | Calculus II | MTH5102_Topic151

Arc Length of a Parametric Curve | Calculus II | MTH5102_Topic152

Finding the Arc Length of a Parametric Curve | Calculus II | MTH5102_Topic153

Understanding Polar Coordinates | Calculus II | MTH5102_Topic154

Converting Between Rectangular and Polar Coordinates | Calculus II | MTH5102_Topic155

Plotting Points in the Polar Plane | Calculus II | MTH5102_Topic156

Polar Curves | Calculus II | MTH5102_Topic157

Area of a Region Bounded by a Polar Curve | Calculus II | MTH5102_Topic158

Finding the Area Between Two Polar Curves | Calculus II | MTH5102_Topic159

Arc Length in Polar Curves | Calculus II | MTH5102_Topic160

Finding Arc Length of a Polar Curve | Calculus II | MTH5102_Topic161

Introduction to Conic Section | Calculus II | MTH5102_Topic162

Definition and Equation of Parabolas | Calculus II | MTH5102_Topic163

Standard and General Forms of a Parabola | Calculus II | MTH5102_Topic164

Standard and General Forms of a Parabola: Examples | Calculus II | MTH5102_Topic165

Understanding Ellipses | Calculus II | MTH5102_Topic166

Finding the Standard from of an Ellipse | Calculus II | MTH5102_Topic167

Application of Ellipses | Calculus II | MTH5102_Topic168

Equation of a Hyperbolas in Standard Form | Calculus II | MTH5102_Topic169

Finding the Standard Form of a Hyperbola | Calculus II | MTH5102_Topic170

Eccentricity and Directrix | Calculus II | MTH5102_Topic171

Determining Eccentricity of a Conic Section | Calculus II | MTH5102_Topic172

Polar Equations of Conic Sections | Calculus II | MTH5102_Topic173

Identifying a Conic Section in Polar Coordinates | Calculus II | MTH5102_Topic174

General Second-Degree Equations and Rotated Conic Sections | Calculus II | MTH5102_Topic175

Identifying Rotated Conic | Calculus II | MTH5102_Topic176