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Introduction to Differential Calculus

Learn about differential calculus in mathematics, its formulas as well as its application in this free online course.

Publisher: ADU
This course on differential calculus will provide you with a comprehensive guide to the different methods of obtaining the derivatives of a function. You will learn how to calculate the rates of change in calculus and understand the definition of a derivative and notation. You will also learn about the derivatives of trigonometric functions in differential calculus. Start this course now and improve your skills in differential calculus.
Introduction to Differential Calculus
  • Duration

    3-4 Hours
  • Students

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Differential calculus is a subfield of calculus in mathematics. This course introduces you to the concept of differential calculus and the various ways to calculate rates of change in calculus. Next, examine how to obtain the slope of a curve at a point and the slope of the tangent to a curve. Learn about the characteristics of a normal curve in differential calculus and how to calculate it. Then we discuss the derivative definition and notation, the usefulness of each notation in a differential equation, the different notations for and the processes of finding the derivative of a function. We include how to keep a multiplicative constant in differential calculus. We outline the different ways of obtaining a one-sided derivative, the concept of continuity and differentiability in calculus. Finally, you will discover the importance and the use of the intermediate value theorem in differential calculus.

This course will then introduce you to the different differentiation methods in differential calculus. You will specifically learn about the power rule, the quotient rule, the product rule, the sum and the different rules of differentiation and the various ways to obtain the derivatives of trigonometric functions in differential calculus. Investigate how to differentiate a parametrized curve in an equation, how the differentiating implicitly defined functions work in calculus and how to obtain the derivatives of logarithmic functions in differential calculus. You will then learn how to differentiate a composite function at any point in its domain using the composite function and the chain rule. This course will teach you why the rates of change of a function at a specified point change in an equation due to the higher-order derivative method of differential calculus. You will also learn about the inverse function of the sine, otherwise known as the ‘arcsine function’, the arctangent function of trigonometry function of derivatives along with the function of the remaining inverse function of calculus. This course describes how to identify and obtain the concavity and points of inflection in differential calculus.

Finally, this course demonstrates the different matching functions graphically in differential calculus with their derivatives. We discuss the concept of the ‘local extreme value’ theorem and how to use a graph to find extrema in differential calculus. You will also learn about a function’s maxima and minima, which means the maximum and minimum function that makes up the extrema in differential calculus. You will become familiar with the critical points in differential calculus, using the ‘mean value’ theorem and Rolle’s theorem’s position as a differentiation method in identifying a point where the first derivative is zero in an equation, including the second derivative function. You will then learn about the concepts and the relationships between velocity, acceleration and jerk in differential calculus. This course will teach you how to solve related rate problems involving finding the rate at which the quantity changes by relating that quantity to other quantities. We will improve your knowledge of applying derivatives using the linear approximation formula of differential calculus. Begin this course today and expand your mastery of differential calculus.

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