Basic Mathematics

Birla Institute of Technology & Science, Pilani via Coursera

Go to Course: https://www.coursera.org/learn/basicmathematics

Introduction

### Course Review: Basic Mathematics on Coursera Mathematics serves as the foundation for many disciplines, and for those looking to solidify their understanding or brush up on essential math skills, the **Basic Mathematics** course on Coursera stands out as an exceptional choice. Designed for beginners, this course introduces a range of fundamental topics that are crucial for both academic pursuits and real-world applications. #### Course Overview The Basic Mathematics course provides a comprehensive introduction to vital mathematical concepts, including **Complex Numbers**, **Quadratic Equations**, **Trigonometry**, **Matrices**, **Differential Calculus**, **Integral Calculus**, and **Ordinary Differential Equations**. Each topic is carefully structured to build upon previous knowledge, allowing learners to grasp complex ideas progressively. **Course Syllabus Highlights:** 1. **Course Introduction**: The journey begins with an overview of the course structure, objectives, assessments, and live session details. This foundational module not only sets clear expectations but also encourages students to interact with peers globally, fostering a collaborative learning environment. 2. **Complex Numbers & Quadratic Equations**: This module delves into the real and complex number systems, offering insights into properties, algebra, and various forms of equations. A strong understanding of these concepts is critical as they form the basis for higher-level mathematics. 3. **Trigonometry**: A vital area of study, trigonometry is explored through its fundamental identities and applications. This module helps demystify the relationships between angles and sides of triangles and introduces students to critical applications in physics and engineering. 4. **Matrices**: Matrices play a significant role in data analysis and computer science. In this module, students learn definitions, types, and algebraic operations on matrices, along with methods to solve systems of equations, which are invaluable skills in numerous applications. 5. **Differential Calculus with Applications**: This module offers a deep dive into functions, continuity, differentiability, and the mean value theorem. Understanding calculus is essential for advanced studies in almost all scientific fields, making this section particularly beneficial. 6. **Integral Calculus with Applications**: Following differential calculus, this module explores integration, a key aspect of calculus, with practical applications that enhance problem-solving skills. 7. **Ordinary Differential Equations**: The course concludes with a thorough introduction to differential equations, essential for anyone pursuing a career in engineering, physics, or mathematics. #### Course Format and Interaction The course is presented through a mix of video lectures, reading materials, and practical assessments designed to facilitate active learning. Each module includes exercises to test comprehension and reinforce skills, allowing students to apply what they've learned in real-world scenarios. There are also opportunities for peer interaction and feedback, making the learning experience dynamic and engaging. #### Final Thoughts The **Basic Mathematics** course on Coursera is highly recommended for anyone interested in strengthening their mathematical foundation, whether as a stepping stone for further studies or simply to enhance everyday problem-solving skills. The structured approach, paired with interactive elements and practical applications, ensures that participants emerge with a solid grasp of essential mathematics concepts. In a world where quantitative reasoning is increasingly important, investing time in this course can yield substantial benefits, providing you with the tools necessary to succeed in both academic and professional settings. With no prior knowledge required, this course is accessible to all, making it an excellent resource for lifelong learners. Enroll today and take the first step towards mastering the basics of mathematics!

Syllabus

Course Introduction

This module introduces you to the course and its syllabus. The course introductory video orients you to the skills and knowledge you will acquire through this course. The syllabus reading highlights the course values, assessments, grading scheme, schedule and details of live sessions, and readings list that you must procure to acquire the concepts better. You will also meet and greet your peers around the globe through a discussion prompt.

Complex Numbers & Quadratic Equations

In this module we will present real & complex number system, properties of complex numbers, algebra of complex numbers, complex conjugate, argand plane, types of equations, roots of quadratic equation.

Trigonometry

In this module, we will present the basics of trigonometry, trigonometric identities and applications of trigonometry.

Matrices

In this module, we will present definition, types of matrices and also learn algebraic operations on matrices, finding inverse of a matrix. Also given system of equations we will learn finding its solution and also rank of a given matrix.

Differential Calculus with applications

In this module, we will present functions, types of functions, definition of limit, standard form, standard limits, indeterminate forms, continuity and differentiability, derivative of standard functions, applications of derivatives, mean value theorem.

Integral Calculus with Applications

In this module, we will present integral of a function, integrals of standard functions, properties, product rule, division rule, applications of integration.

Ordinary Differential Equations

In this module, we will present types of differential equations, order and degree of a differential equation, First order and first degree differential equation solutions - variable separable, Homogeneous and Non homogeneous equation, exact and non – exact differential equation, first order linear differential equations.