BASIC CALCULUS

Basic Calculus

The Basic Calculus module is designed to introduce students to the foundational concepts and principles of calculus. This module aims to develop students' understanding of key calculus concepts, including limits, derivatives, and integrals, and their applications in solving real-world problems in various fields like physics, engineering, economics, and biology.

Students will learn the fundamental ideas behind calculus, starting with the concept of a limit, which forms the basis for understanding continuity and derivatives. The module will then explore the concept of the derivative, which describes the rate of change of a function, and how to calculate it using basic differentiation techniques. The second major area covered will be integrals, which are used to find the area under curves and solve problems related to accumulation and totals.

The course emphasizes problem-solving and critical thinking, using calculus tools to solve practical problems and develop a deeper understanding of mathematical relationships. By the end of the module, students will have the skills to apply calculus concepts to solve problems involving rates of change and areas under curves.

Key Topics Include:

• Introduction to Limits: Understanding the concept of a limit and how it forms the foundation for derivatives and integrals. Exploring the notation and methods of evaluating limits.

• Continuity: Understanding the continuity of a function and how it relates to limits.

• Derivatives: Learning about the derivative of a function, including how to compute it using rules such as the power rule, product rule, quotient rule, and chain rule. The module will explore applications of derivatives, such as finding the slope of curves, motion problems, and optimization problems.

• Applications of Derivatives: Using derivatives to solve real-world problems such as finding rates of change, maxima and minima of functions, and related rates in physics and other fields.

• Integrals: Introducing the concept of integration as the inverse process of differentiation. Students will learn how to compute indefinite integrals (antiderivatives) and definite integrals, and understand their applications in calculating areas under curves, distances, and accumulated quantities.

• Fundamental Theorem of Calculus: Understanding the connection between differentiation and integration through the fundamental theorem of calculus.

• Techniques of Integration: Exploring basic techniques for integrating functions, such as substitution and integration by parts.

• Applications of Integrals: Using integrals to solve practical problems, including finding areas, volumes, and other accumulated quantities in fields such as physics, engineering, and economics.

Through a combination of theory, examples, exercises, and real-world applications, students will gain a strong understanding of basic calculus principles. By the end of the module, students will be able to apply calculus concepts in problem-solving and appreciate its significance in various academic and professional fields.