Differential Calculus From Scratch

Differentiation, Limits, Application of derivatives

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What You Will Learn!

Understand basic concepts of limits and evaluate trigonometric limits, limits at infinity. check the existence of limit of a function.
Verify the continuity of a function at a point and in an interval.
Perform differentiation from first principles
Evaluate the derivative of functions, product of functions, quotient of two functions and function of a function.
Perform differentiation of implicit functions, logarithmic functions and infinite series.
Perform differentiation of parametric functions and derivative of one function w.r.t. another function
Evaluate derivatives of higher order.
Solve the problems based on application of derivatives
Understand and verify Rolle’s and Lagrange’s mean value theorems
Find the equations of tangents and normals to a curve at a point using differentiation.
Verify whether a function is increasing or decreasing
Find the points of local maxima and minima using first derivative test, second derivative test and applications of the concept of maxima and minima

Description

This course has been designed for class 11 and 12 students. All the concepts of differentiation are explained along with solved examples. Lots of problems are solved to make the students confident to solve the problems. Questions of all levels of difficulties are solved. Efforts have been made to make the complex concepts simple and easy for students. Concepts of differentiation not only form a major portion of mathematics but also have applications in physics

The following topics are covered in this course:

1. Limits: Basic concepts, trigonometric limits, limits at infinity, existence of limit of a function.

2. Continuity: Continuity at a point, Continuous functions

3. Differentiability: Right hand derivative and left hand derivative, differentiability of a function.

4. Differentiation: Differentiation from first principles, derivative of functions, derivative of the product of functions. Derivative of quotient of two functions, derivative of a function of a function. Differentiation of implicit functions, differentiation of logarithmic functions, differentiation of infinite series. Differentiation of parametric functions, derivative of one function w.r.t. another function, derivatives of higher order.

5. Application of derivatives

6. Rolle’s and Lagrange’s theorems

7. Tangents and normals.

8. Monotonic functions: Increasing and decreasing functions

9. Local maxima and local minima: first derivative test, second derivative test, applications of the concept of local maxima and minima

Course Title: Differential calculus from scratch(For grade 11 and 12)

Prerequisite: Basic Algebra and trigonometry of grade 10

Duration of course : 23hr 15 min