Introduction to Differential Calculus
Learn about differential calculus in mathematics, its formulas, as well as its application in this free online course.Publisher: ADU
CertificationView course modules
This free online course on differential calculus, a subfield of calculus in mathematics will begin by introducing you to the concept of differential calculus along with the various ways to calculate rates of change in calculus. You will learn how to obtain the slope of a curve at a point along with the slope of the tangent to a curve. This course will then teach you about the characteristics of a normal curve in differential calculus as well as how to calculate a normal curve. You will also learn about the definition of derivative and notation, the usefulness of each notation in a differential equation along with the different notations for and the processes of finding the derivative of a function, including how to keep a multiplicative constant in differential calculus, different ways of obtaining a one-sided derivative, the concept of continuity as well as differentiability in calculus, the importance, and the use of intermediate value theorem in differential calculus.
This course will then introduce you to the different methods of differentiation in differential calculus. You will specifically learn about the power rule, the quotient rule, the product rule, the sum and the different rule of differentiation, as well as the various ways to obtain the derivatives of trigonometric function in differential calculus. You will further learn how to differentiate a parametrized curve in an equation, how the differentiating implicitly defined functions work in calculus, along the ways 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 as well as the chain rule. This course will teach you why the rates of change of a function at a specified point changes in an equation as a result of 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 will also teach you how to identify as well as obtain the concavity and points of inflection in differential calculus.
Finally, this course will introduce you to the different ways of matching functions with their derivatives graphically in differential calculus. You will learn about the concept of the local extreme value theorem as well as how to use a graph to find extrema in differential calculus. You will also learn about the maxima and minima of a function which means the maximum and minimum function that makes up the extrema in differential calculus. This course will then teach you about the critical points in differential calculus using the mean value theorem as well as the position of Rolle’s theorem as a method of differentiation 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 along with the relationships between velocity, acceleration, and jerk in differential calculus. This course will finally teach you how to solve related rate problems that involve finding the rate at which the quantity changes by relating that quantity to other quantities. This course is set to improve your knowledge of the application of derivatives using the linear approximation formula of differential calculus. Begin this course today and expand your knowledge of differential calculusStart Course Now
Differential Calculus - Learning Outcomes
Introduction to Differential Calculus
Derivative and Notation
Differential Calculus - Lesson Summary
Methods of Differentiation
Methods of Differentiation - Learning Outcomes
Introduction to Methods of Differentiation
Derivatives of Trigonometric Functions
Implicit Functions and Implicit Differentiation
Derivatives of Inverse Trigonometric Functions
Derivatives of Logarithmic Functions
Methods of Differentiation - Lesson Summary
Graphs of Functions and Their Derivatives
Graphs of Functions and Their Derivatives - Learning Outcomes
Increasing and Decreasing Functions
Velocity, Acceleration and Jerk
Graphs of Functions and Their Derivatives - Lesson Summary
Upon the successful completion of this course, you should be able to:
- Discuss the rates of change in differential calculus.
- Identify the slope of a curve at a point and the slope of the tangent to a curve.
- Discuss the definition of a derivative and notation in differential calculus.
- Explain the various methods of differentiation.
- Discuss how to differentiate a parameterized curve in differential calculus.
- Analyze the derivatives of inverse trigonometric functions.
- Explain the concepts of maxima, minima, and extrema as they relate to differentiation.
- Discuss the relationships between f(x), f'(x) and f"(x) in differentiation.
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