Fundamentals of Calculus - Linkeducare

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The course is largely an extension of basic calculus courses. Topics discussed include: Integrals, sequences, series, functions of several variables, partial derivatives, double integrals.

The affiliated University will issue a course completion certificate on course completion and if an online exam is passed. If no exam is taken, the affiliated University will issue a certificate of course attendance.

Course Content

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Basic of integrations and substitution method 4 Presentations

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Understand the basic rules of definite and indefinite integrals

Solve integrals using substitution method, application on exponential functions

Solve integrals involving logarithmic functions

General Exercises

Integration by parts 3 Presentations

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understand when and how we use the integration by parts method to calculate the integral

Tabular of integration: Forms 1 and 2

General Exercises

Trigonometric integrals 3 Presentations

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Apply integrals involving sines and cosines

Apply integrals involving tanx and sec x

General Exercises

Integration using trigonometric substitution 3 Presentations

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Solving integrals using trigonometric substitutions case 1

Solving integrals using trigonometric substitutions case 2

Solving integrals using trigonometric substitutions case 3

integration using partial fraction method 2 Presentations

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Solving integrals using partial fraction methods

Heaviside method to calculate the coefficients

Inverse trigonometric functions 4 Presentations

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Definition of inverse trigonometric functions

Calculate the inverse trigonometric of a number

Derivatives of inverse trigonometric functions

Integrals of inverse trigonometric functions

Hyperbolic functions 3 Presentations

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Definition of hyperbolic functions

Derivatives and integrals of hyperbolic functions

Definition of inverse hyperbolic functions, integrals and derivatives of inverse hyperbolic

Sequences 1 Presentation

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Convergence and divergence of sequences

Infinite series 3 Presentations

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Define the infinite series, and test the divergence using N’th term

Identify the geometric series, and test the convergence and divergence of these series

Identify the telescoping series and test the convergence and divergence of these series

Integral test 2 Presentations

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Integral test to identify the convergence and divergence of series

Convergence and divergence of P series

Comparison Tests 2 Presentations

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Define and Use DCT for convergence and divergence

Define and Use LCT for convergence and divergence

Absolute and conditional convergence, root and ratio test 2 Presentations

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Test the absolute convergence or divergence using ratio test

Test the absolute convergence or divergence using root test

Absolute and conditional convergence of Alternating series 2 Presentations

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Identify the Alternating series and understand the test related to alternating series called “AST

Understand the difference between absolute and conditional convergence

Power series 2 Presentations

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Find the radius of convergence of a series

Operations performed on power series

Maclaurin and Taylor series 3 Presentations

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Define the Maclaurin series and Find its expression for well-defined functions f(x)

Define Taylor polynomials

Use of Taylor and Maclaurin series

Function of multiple variables: Domain, range and level curves 3 Presentations

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Find and sketch the domain of definition of a function

Find the range of a function

Find and sketch the level curves of a function

Partial derivatives and chain rules 2 Presentations

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Define the partial derivatives of first and second order for functions of two variables.

Apply the chain rule to calculate the derivatives in 3 cases

Gradient of a function and its applications 2 Presentations

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Calculate the differential of a function, gradient of a function and calculate the directional derivatives

Find the tangent plane of a function at a given point

Double integrals 2 Presentations

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Double integrals over a general region.

Double integrals over a rectangular region.