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Logic and Set Theory

16 videos · 53m 34s

Operations on Sets

17 videos · 51m 36s

Irrational Numbers

9 videos · 33m 43s

Bounded and Unbounded Sets in R

23 videos · 1h 17m 33s

Further properties of bounded sets

18 videos · 1h 6m 16s

Mathematical Induction

15 videos · 1h 8m 36s

Summation and Sigma notation

8 videos · 36m 42s

The Real Number System

10 videos · 34m 19s

Famous Inequalities

10 videos · 36m 6s

The Concept of a Function

7 videos · 51m 46s

Common Functions

6 videos · 35m 17s

The Domain of Definition of a Function

1 video · 4m 56s

The Domain of Basic Functions

8 videos · 10m 54s

The Domain of Logarithmic and Exponential Functions

5 videos · 18m 45s

The Domain of Trigonometric Functions

5 videos · 6m 4s

The Domain of Absolute Value Functions

2 videos · 3m 36s

The Domain of a Piecewise Function

1 video · 4m 33s

Translation (Shifting) and Reflection of Functions

16 videos · 1h 43s

The Composition of Functions

13 videos · 35m 48s

Even and Odd Functions

16 videos · 37m 24s

One-to-One Functions

10 videos · 30m 12s

The Inverse of a Function

13 videos · 1h 24m 12s

Piecewise-Defined Functions

7 videos · 46m 5s

The Absolute Value Function

4 videos · 13m 57s

Introduction

1 video · 10m 15s

Technique 1 Substitution

5 videos · 11m 56s

Technique 2 Factoring

5 videos · 22m 43s

Technique 3 Multiplying by the Conjugate

8 videos · 48m 59s

Technique 8 The Sandwich Squeeze Theorem

11 videos · 51m 20s

Technique 9 Piecewise Functions

6 videos · 21m 37s

Technique 4 Function Tends to Infinity

12 videos · 29m 4s

Technique 5 X Tends to Infinity

25 videos · 1h 43m 50s

Technique 6 Eulers Limit

10 videos · 54m 36s

Technique 7 Trigonometric Limits

12 videos · 59m 39s

Limit from Definition

26 videos · 2h 25m 5s

Summarizing Questions

4 videos · 8m 42s

Basic Derivatives of Functions

11 videos · 1h 54m 48s

Derivative of Exponents and Logarithmic Functions

7 videos · 53m 36s

Trigonometric Derivatives

3 videos · 36m 58s

Derivative of Power Functions

4 videos · 1h 29m 38s

Implicit Differentiation

5 videos · 1h 31m 12s

Calculations Using The Definition of Derivative

6 videos · 49m 55s

The Derivative of an Inverse of a Function

6 videos · 11m 35s

Logarithmic Differentiation

3 videos · 18m 52s

Tangent and Normal Lines - Basic Exercises

16 videos · 1h 44m 11s

Tangent and Normal Lines of Implicit Functions

4 videos · 27m 8s

Tangent and Normal lines - Parametric Functions

3 videos · 17m 20s

The Angle Between Two Curves

4 videos · 25m 47s

Vertical Tangents and Cusps

8 videos · 44m 29s

Linear Approximation

7 videos · 31m 10s

Tangent and Normal Lines – Exercises with a Constant

11 videos · 1h 29m 47s

Summarizing Questions

3 videos · 12m 40s

Extrema, Increase, Decrease

33 videos · 3h 56m 17s

Inflection, Convex, Concave

31 videos · 3h 51m 45s

Vertical Asymptotes

35 videos · 1h 7m 36s

Horizontal Asymptotes

38 videos · 1h 3m 18s

Oblique Asymptotes

37 videos · 2h 18m 18s

Global Extrema

14 videos · 1h 54m 48s

Curve Plotting

10 videos · 1h 7m 35s

Summarizing Questions

12 videos · 37m 4s

Introduction to Definite Integrals

13 videos · 52m 1s

Inequalities

9 videos · 33m 4s

Riemann Sum and Integrability

22 videos · 1h 56m 37s

Fundamental Theorm of Calculus

19 videos · 1h 40m 14s

Riemann Integration and Integrability

19 videos · 2h 24m 42s

Further Exercises - Criterion for Integrability

17 videos · 1h 39m 51s

Advanced exercises - Riemann Sum and FTC

28 videos · 1h 24m 6s

Areas

22 videos · 3h 32m

Curve Length

16 videos · 1h 27m 24s

Work

4 videos · 22m 33s

Center of Mass

3 videos · 17m 3s

Hydrostatic Pressure and Force

2 videos · 17m 59s

Probability

4 videos · 28m 6s

Mean Value Theorem for Integrals

2 videos · 8m 51s

Average Function Value

2 videos · 10m 34s

Numerical Integration

4 videos · 50m 30s

Total: 21 videos · 3h 9m

Introduction

2 videos · 23m 6s

Conversion between Polar and Cartesian Coordinates

7 videos · 1h 14m 12s

Tangent Lines in Polar Coordinates

3 videos · 25m 44s

Arc Length in Polar Coordinates

3 videos · 30m 19s

Area in Polar Coordinates

3 videos · 31m 42s

Surface Area in Polar Coordinates

3 videos · 31m 43s

Infinite Geometric Series

19 videos · 2h 15m 43s

Sequences

6 videos · 45m 45s

The Harmonic Series and The P-Series

2 videos · 16m 56s

Algebraic Properties of Series

1 video · 8m 47s

The Divergence Test

1 video · 9m 44s

The Integral Test

6 videos · 1h 40s

The Alternating Series Test

3 videos · 20m 19s

The Limit Comparison Test

18 videos · 2h 23m 53s

The Ratio Test

9 videos · 1h 11m 22s

Absolute and Conditional Convergence of Series

12 videos · 1h 9m 55s

Introduction to Taylor and Maclaurin Series

7 videos · 1h 14m 51s

Basic Exercises with Maclaurin Series

9 videos · 54m 9s

Expansions about General Point

4 videos · 22m 47s

Finding Nonzero Terms in Expansions

4 videos · 37m 11s

Sum of Series Using Taylor and Maclaurin Expansions

7 videos · 21m 53s

Finding Limits Using Expansions

4 videos · 27m 8s

Computations with Taylor Series

15 videos · 1h 6m 55s

The 3D Coordinates System

5 videos · 33m 40s

Equations of Lines

8 videos · 57m 36s

Equations of Planes

11 videos · 1h 33m 36s

Quadratic Surfaces

6 videos · 33m 15s

Functions of Several Variables

11 videos · 55m 27s

Vector Functions in 3D Coordinates System

6 videos · 44m 48s

Vector Calculus in 3D Coordinates System

3 videos · 28m 52s

Tangent, Normal and Binormal Vectors

7 videos · 1h 2m 50s

Integrals of Vector Functions

1 video · 10m 16s

Arc Length with Vector Functions

5 videos · 35m 57s

Curvatures in 2D and 3D Space

7 videos · 1h 2m 57s

Velocity and Acceleration in Space

6 videos · 1h 10m 44s

Cylindrical and Spherical Coordinate Systems

14 videos · 1h 11m 27s

Introduction

1 video · 23m 8s

Separable Equations

14 videos · 46m 20s

Homogeneous Equations

11 videos · 1h 39s

Homogeneous after Substitution

6 videos · 34m 23s

Exact Equations

8 videos · 47m 21s

Integration Factor

17 videos · 1h 56m 45s

Linear Equations

9 videos · 33m 27s

Ricatti Equations

5 videos · 40m 23s

Existence and Uniqueness

11 videos · 1h 15m 47s

Bernoulli Equations

6 videos · 28m 39s

Missing X or Y, Reduction of Order

9 videos · 39m 39s

Linear, Homogeneous, Constant Coefficients

10 videos · 20m 10s

Linear, Nonhomogeneous, Constant Coefficients - Method of Undetermined Coefficients

15 videos · 1h 30m 47s

Linear, Nonhomogeneous, Constant Coefficients - Method of Variation of Parameters

11 videos · 1h 16m 18s

Eulers Equation

2 videos · 18m 23s

Linear, Homogeneous, Non-Constant Coefficients - 2nd Solution Method

5 videos · 41m 33s

The Wronskian and its Uses

10 videos · 57m 53s

Sturm-Liouville Problems

11 videos · 1h 51m 59s

Introduction to Inner Product Spaces

10 videos · 1h 34m 54s

Norm and Distance

11 videos · 1h 2m 20s

Cauchy–Schwarz Inequality

10 videos · 36m 41s

Orthogonality

10 videos · 33m 6s

Orthogonal Complement

14 videos · 1h 16m 13s

Orthogonal Sets and Bases

12 videos · 1h 3m 4s

Gram Schmitt Process

5 videos · 29m 39s

Orthogonal Matrices

12 videos · 52m 21s

Orthogonal Transformations

17 videos · 1h 7m 5s

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Hey there AERO40006 student!

We have designed this module on Mathematics 1 for those who are studying at Imperial College London and want to consolidate their understanding and learn from experts and professors, at any time, and from anywhere.

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Amos Bahiri earned his undergraduate degree in Mathematics, and then went on to earn two Master’s Degrees (MS) in Mathematics and Computer & Information Science from Ohio State University. In addition to being an outstanding instructor of mathematics, Amos is known for his math jokes.

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