About this course
Mathematics is the language of Science, Engineering and Technology. Calculus is an elementary mathematical course in any Science and Engineering Bachelor. Pre-university Calculus will prepare you for the Introductory Calculus courses by reviewing five important mathematical subjects that are assumed to be mastered by beginning Bachelor students: functions, equations, differentiation, integration and analytic geometry. After this course you will be well prepared to start your university calculus course. You will learn to understand the necessary definitions and mathematical concepts needed and you will be trained to apply those and solve mathematical problems. You will feel confident in using basic mathematical techniques for your first calculus course at university-level, building on high-school level mathematics. We aim to teach you the skills, but also to show you how mathematics will be used in different engineering and science disciplines.

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FUNCTIONS PART 1
0:00:00 Introduction
0:03:38 How to describe a Function
0:08:37 Polynomial Function
0:13:38 Graphs of Polynomial Functions
0:19:52 Rational Function
0:28:32 Power Function with Integer exponent
0:34:51 Power Function with non-interger exponent
0:40:26 Power Function - Catch the Error
0:41:40 Power Function - Catch the Error
0:43:58 Domain and Range
0:49:14 Continuity
0:55:10 Summary Polynomial

FUNCTIONS PART 2
1:02:51 Taylor Polynomials
1:08:29 Trigonometric Functions
1:16:25 How to Calculate with Trigonometric Functions
1:22:30 Trigonometric Functions - Catch the Error
1:24:11 Trigonometric Functions - Cathc the Error
1:26:04 How to compose Functions
1:30:22 Calling and Translation
1:35:55 Exponential Functions
1:41:06 Inverse Funtions
1:47:09 Logarithms
1:53:06 How to Calculate with Logarithms
1:58:54 Summary Trignometric and Exponential Functions

EQUATIONS PART 1
2:07:15 Fourier Series
2:10:27 Proton therapy
2:15:24 Equations of Polynomials degree 1 and 2
2:21:15 Equations of Polynomials degree 3 and higher
2:26:33 Equations involving Fractions
2:33:15 Equations involving square roots
2:37:15 Solving equations, general techniques
2:44:13 Solving Equations - Catch Error - Equations
2:45:50 Solving Equations - Catch Error - Explanation
2:46:52 Summary solving equations

EQUATIONS PART 2
2:52:34 Complex numbers
2:57:55 Trigonometric equations
3:05:57 Equations involving exponentials and logarithms
3:11:43 Solving Equations containing logarithms - Catch The Error
3:16:27 Solving inequalities
3:22:59 Solving Ineqaulities - Catch the Error - Equations
3:26:24 Solving inequalities - Catch the Error - Explanation
3:28:29 System of equations
3:34:58 Summary solving (in) equalities

DIFFERENTIATION
3:38:43 Linear programming and optimization
3:42:47 Roller Coaster
3:44:39 Definition of derivative
3:51:11 How to Determine the derivative
3:54:01 Product rule and chain rule
3:59:19 Product rule and chain rule
4:09:21 52Derivative of x^p and a^x
4:15:55 How to determine the derivative
4:18:45 Non-differentiable functions
4:22:00 Optimization - Finding minima and maxima
4:33:21 Finding minimum or maximum - Catch the Error - Explanation
4:34:21 Summary Derivatives

INTEGRATIONS
4:38:40 Differentia Equation
4:44:07 Pret-a-loger - integration
4:46:28 Riemann sum - integration
4:52:36 The meaning of the integral
4:55:57 Fundamental theorem of Calculus
5:03:15 Proof of fundamental theorem of Calculus
5:13:27 Rules of Calculation - Spitting the interval
5:19:01 Rules of Calculation - linear Substitutions
5:22:42 Integral - Catch The Error - integration
5:24:12 Integral - Catch The Error - Explanation
5:25:30 Summary integrals

What you'll learn
Understand, visualize and manipulate different elementary functions, like power functions, roots, polynomials, trigonometric functions, exponential and logarithmic functions;
Understand, visualize and solve equations and inequalities involving these elementary functions;
Understand the concept of differentiation and calculate the derivatives of compositions of elementary functions;
Understand the concept of integration and to use some elementary integration techniques;
Understand, visualize and manipulate geometric objects in the plane, such as vectors, lines, circles and more general curves.

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⌨️ This course is created in collaboration with (TU Delft)

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