Calculus Materclass: From Theory To Real-World Applications

Unlocking the Power of Calculus:A Comprehensive Guide to Solving Complex Problems in Science, Engineering, and Economics

What you'll learn

Develop a strong foundation in calculus concepts and techniques - learn the fundamentals of limits, derivatives, and integrals.

Improve problem-solving skills in calculus - apply calculus techniques to solve a variety of mathematical problems.

Understand the practical applications of calculus - explore real-world examples of how calculus is used in various fields, including physics, engineering….

Build confidence in calculus - gain the skills and knowledge needed to tackle more advanced calculus topics with ease.

Requirements

Brush up on algebra and trigonometry - although not required, having a solid foundation in these subjects will make it easier to understand calculus concepts.

Practice, practice, practice - calculus requires practice and repetition to master, so learners should be prepared to work through many problems and exercises to build their skills and confidence.

Description

Calculus is a fundamental branch of mathematics that has a wide range of applications across various fields, from natural sciences to engineering and economics. This masterclass provides a comprehensive introduction to calculus, covering its fundamental principles and real-world applications.The masterclass will start with an overview of limits, derivatives, and integrals, which form the foundation of calculus. Through this, you will learn how to apply calculus to solve problems related to rates of change and optimization. Building on these concepts, the masterclass will delve into more advanced topics such as multivariable calculus, differential equations, and optimization techniques.Multivariable calculus is a branch of calculus that deals with functions of more than one variable. Differential equations involve finding functions that satisfy specific conditions, and optimization techniques allow for the efficient and effective use of resources in various processes. You will learn how these topics apply to real-world problems and develop the necessary mathematical concepts, such as the chain rule and the fundamental theorem of calculus, to solve these problems.The masterclass will also provide case studies from various fields to illustrate how calculus can be applied to solve practical problems. Through those examples, you will see firsthand how calculus can be applied to real-world situations and gain a deeper understanding of how to approach complex problems.Whether you are a student seeking to improve your calculus skills or a professional looking to apply calculus to your work, this masterclass will equip you with a strong foundation in calculus theory and the practical skills necessary to apply it to real-world problems. By the end of this masterclass, you will have the knowledge and skills needed to solve complex problems in various fields using calculus.

Overview

Section 1: Welcome to the course

Lecture 1 Course Contents

Section 2: Limits, Continuity, Differentiability

Lecture 2 Limits (Algebraically)

Lecture 3 Visualize Limits Geometrically

Lecture 4 Continuity and Differentiability

Section 3: Derivatives and their applications

Lecture 5 Derivative Rules and Formulas

Lecture 6 Derivatives Algebraically and Geometrically

Lecture 7 Application of Derivatives

Section 4: Integrals and Their Applications

Lecture 8 Indefinite integrals

Lecture 9 Definite Integrals

Lecture 10 Integration Techniques

Lecture 11 Application of Integrals

Section 5: Sequences and Series

Lecture 12 Sequences

Lecture 13 Series 1

Lecture 14 Series 2

Lecture 15 Integral and Comparison Test

Lecture 16 Taylor Series

Lecture 17 Application of Series

Section 6: Derivatives and Integrals ( Advanced )

Lecture 18 Partial Derivatives

Lecture 19 Double and Triple Integrals

Lecture 20 Applications of Multiple Integrals

Lecture 21 Line Integrals

Lecture 22 Green's Theorem

Lecture 23 Applications of Line Integrals

Lecture 24 Divergence and Curl

Lecture 25 Calculus with Parametric Equations

Lecture 26 Calculus with Polar Coordinates

Lecture 27 Calculus with Vector Functions

Lecture 28 Arc Length

Section 7: Fourier Analysis and Laplace Transform

Lecture 29 Fourier Series

Lecture 30 Fourier Transform

Lecture 31 Application of Fourier Analysis

Lecture 32 Laplace Transform

Lecture 33 Applications of Laplace Transform

Section 8: Differential Equations

Lecture 34 First Order Differential equations

Lecture 35 Separable Differential Equations

Lecture 36 Homogenous Differential Equations

Lecture 37 Linear Differential Equations

Lecture 38 Exact Differential Equations

Lecture 39 Bernoulli Differential Equations

Lecture 40 Second Order Differential Equations

Lecture 41 Differential Equations with Constants in Coefficients

Lecture 42 Applications of Differential Equations

This course is designed for learners who are interested in building a strong foundation in calculus and developing the skills needed to solve a wide range of mathematical problems. The course will cover all the fundamental calculus topics from limits to derivatives, integrals, and applications of calculus in various fields such as physics, engineering, and economics. The course is ideal for high school and college students, as well as anyone who is interested in improving their math skills and preparing for further study in math, science, or engineering. Learners who have some prior knowledge of algebra and trigonometry will find the course content most accessible, but beginners who are willing to put in the effort can also benefit from the course. Whether you are pursuing a degree in a math or science field or simply interested in improving your mathematical skills, this course will provide you with the knowledge and practice needed to succeed. By the end of the course, you will have a solid foundation in calculus concepts and techniques and be able to apply them to solve a variety of mathematical problems in real world..