
calculus masterclass presents six sections—functions, limits and continuity, derivatives, applications of derivatives, tangents and normals, and increasing and decreasing—each with notes, quizzes, and step-by-step video solutions.
Understand the function as a rule that assigns each element of set A to a corresponding element in set B. Examples include x maps to 2x and x^2+1.
Explore the difference between closed and open intervals on the number line, including how brackets indicate inclusion of endpoints and examples from 1 to 2.
Define domain of a function as the set of x for which the function is defined. Apply rules nonnegative values under square root and intersect domains for combined expressions.
Determine the domain by ensuring the expression under the square root is nonnegative and any denominator is nonzero, yielding intervals such as [-1, infinity) and (-infinity, -3] union [3, infinity).
Explore how to categorize functions by type—from constant and identity to polynomial, rational, exponential, logarithmic, trigonometric (sine, cosine, tangent), analytic, and root functions—along with domain rules.
Learn how a constant function equals a fixed real value k, independent of x, with a horizontal line at y = k and domain as all real numbers.
Explore the identity function, where f(x)=x, represented by the line y=x at 45 degrees, with domain and range all real numbers.
Polynomial functions take the form a0 + a1 x + a2 x^2 + ... + an x^n, with real constants and nonnegative degree n, and domain is all real numbers.
Describe rational functions as the ratio of two polynomials, with the domain restricted by denominator zeros. Identify that p(x)=x^2-3x+5 and q(x)=x^2-3x+2 yield domain all real numbers except x=1 and x=2.
Examine exponential functions of the form a^x with a>0 and a≠1, highlighting growth for a>1 and decay for 0<a<1, and noting domain and positive range.
Interested to have a mastery in Calculus 1? Then this course is definitely for you.
I have been teaching Calculus for 15 years and in this course, I have put up my best efforts to make learning Calculus as simple as possible.
I will be taking you step-by-step from the Foundation of Calculus to the application of derivatives. With every tutorial you will gain crystal clear concept of how Calculus has been designed and how to solve complex mathematics questions by Calculus.
This course has 180 lessons which includes both videos and explanatory notes of everything in Calculus 1. It has 42 quizzes to help you to check yourself how much you have understood the concept. The lessons in the videos has been taught in a very simple manner to let you have a strong hold from basics of Calculus to the Mastery in Calculus.
I have organized Calculus 1 Masterclass in 4 Sections:
Foundation of Calculus (Functions)
Limits and Continuity
Derivatives
Application of Derivatives
Tangent and Normal
Increasing and Decreasing
What this Course Includes:
Videos: The videos are created in such a form to let you understand Calculus and make it as simple as possible. With every topic video there are videos which will explain the problem examples based on that topic. These example videos will increase your concept of that topic of how to apply and what steps to be taken while solving such problems or questions.
Notes: Each section has its own explanatory notes. The notes of each topic contain the detail explanation of topic with graphical explanation to your concept as much clear as possible. These notes will also help you in your academic exams.
Quizzes: The best way to check your concept is to attempt quizzes. That’s why in every section there are quizzes for only that particular topic, so that you can check your knowledge and how much you have understood that topic. If your score is good, you have understood and if your score is not satisfactory, you can view the videos and notes again or ask me in Q&A section.
Quiz Solutions for quizzes in each section: In each section there are quizzes. So, after solving the questions in the quizzes you might need their complete solutions, don’t worry! I have provided complete solutions of each quiz in each section.