HERE IS A METHOD THAT IS HELPING STUDENTS LEARN DIFFERENTIAL CALCULUS
In this world, where Calculus seems difficult, I call upon you to embark on the path to understanding Mathematics better. If you are a student of Mathematics, studying in Class 12, this is your page!
Here are a number of free resources in Differential Calculus which start from the basic properties of logarithm, Continuity and Differentiability.
What you need to do is to use these resources and get a basic understanding of Differential Calculus.
With my years of experience as a High School Math teacher, I can assure you that the links on this page will bring you rich dividends .
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PROPERTIES OF LOGARITHM
Do you know that logarithms are used extensively in Calculus, be it limits, derivatives or Integration? How then do you apply properties of logarithms while solving problems in Calculus? Learn this by watching this video. Here, we discuss the basic properties of logarithms such as the product rule, quotient rule, exponent rule. We also learn how to apply the change of base formula and a few formulae on exponential limits.
MORE ABOUT CONTINUOUS FUNCTIONS
You will learn to solve more problems on continuous functions and find the parameters when the functions are continuous.
Problems are solved for you to learn and practice.
CONTINUITY AT A POINT
Discuss the continuity of Modulus of x. If f(x)= x^3 +3 , if x is not equal to 0, f(x) = 1,when x = 0, discuss the continuity of f at x = 0. If f(x) = x, if x is lesser than or equal to 1, f(x) = 5, if x is greater than 1, discuss the continuity of f at x = 1. If f (x ) = k x ^2, if x is lesser than or equal to 2, f(x) = 3, if x is greater than 2, Find k, if f is continuous at x = 2. Watch all this and more ! Here, you will learn how to check if a function is continuous at a point. It is an integral part of Class 12 Mathematics. You will be introduced to Continuity at a point, left hand and right hand limits for Continuity. Have you ever wanted to be introduced to Calculus. This video will lead you into the basic fundamentals of Calculus. You will learn about continuous functions, left hand limits, right hand limits and continuity at a point. A very useful video for ISC and CBSE students of class 12. Online tutoring is provided for further help. You could register for a masterclass or the entire course.
DERIVATIVE AT A POINT USING THE DEFINITION
Learn more about continuity in this lesson. You will be introduced to left hand and right hand limits, and derivative of a function at a point. Here, you will see the use of limits in calculating the derivative.
HOW TO FIND THE LEFT AND RIGHT HAND DERIVATIVE OF A FUNCTION
More about calculating the derivative using the definition. You will use limits and the concept of left and right hand limits.
Here, you will learn how to evaluate the left hand and right hand derivative at a point. You will also learn a few basic formulas used in Differentiation. This is followed by solved problems for you to practice and learn.
DIFFERENTIATION USING THE PRODUCT RULE
We use the product rule for differentiation. We also learn the importance of simplifying the function before differentiating it.
2 solved problems are shown in the link below.
DERIVATIVE OF COMPOSITE FUNTIONS
Learn how to use the chain rule in deriving composite functions. What is a composite function? A function in a function! Use the normal formula and multiply by the derivative of the function.
MORE ABOUT COMPOSITE FUNCTIONS
This lesson will enhance your understanding of the Chain rule. As a takeaway, you will be prepared to handle more rigorous topics in Differentiation such as implicit functions and logarithmic functions.
WHAT ARE IMPLICIT FUNCTIONS AND HOW DO YOU DERIVE THEM
What is the difference between an explicit and implicit function and how do you differentiate them?
MORE ABOUT IMPLICIT FUNCTIONS
Continuing your study of differentiability with this lesson. This lesson covers Implicit Functions and how to differentiate them. Being a mathematics educator for close to three decades, I hope to make math easy for you through these lessons. This lesson prepares you to handle differentiation of logarithmic functions and higher order differentiation in general. Not to mention, it would greatly help students of class 12 l, ISC and CBSE boards who are learning mathematics.
SECOND ORDER DERIVATIVES
Here, you will be introduced to problems on Second Order Derivatives. Rolle's Theorem and its geometrical application is also introduced. In Class 12 Mathematics, you are generally asked to solve a lot of identities in Differentiation , involving second order derivatives. This lesson prepares you for this. There is also the statement of Rolle's Theorem with its geometrical implication which is introduced. This lesson is aligned with the class 12 syllabus which only focuses on application of Rolle's Theorem. Hence, the proof of Rolle's Theorem is not mentioned. I am a math educator teaching mathematics for over two decades. I have tried to simplify this topic for you. This lesson is a good takeaway for Class 12 students of the ISC, CBSE or any other board.
DERIVATIVE AS A RATE MEASURE
Learn how you can calculate derivative as a rate measure in this video. You will learn how to apply derivatives in real life situations. You will use geometry and derivatives to calculate how to find the rate of change in the derivative. Being a math educator for close to three decades, I have tried to simplify this for you in this video. This topic is slightly tricky as you need to understand the problem first
MORE PROBLEMS ON DERIVATIVE AS A RATE MEASURE
Here, you will learn how to work out problems using derivative as a rate measure. You will learn how to calculate the rate of change of the variables in each problem. We touch upon problems in Geometry like a cone and sphere. Some of the problems discusses include: If an edge of a cube is increasing at a certain rate, at what rate is the volume increasing? If a girl of a certain height walks away from a lamppost, how much is the length of her shadow increasing? Online classes are also provided. You can choose between specific topics or the entire course. MCQS and case study questions are also included. You can contact me on firstname.lastname@example.org
INCREASING AND DECREASING FUNCTIONS
Here is another video on Applications of Derivatives for you!. Here, I will be decreasing increasing, strictly increasing, decreasing and strictly decreasing functions and how to determine the interval in which these functions are increasing or decreasing. Again, we go back to quadratic inequalities and use that to determine the interval.
Presenting as many formulas as possible to give you a quick revision before your exams. This lesson deals with formulas for Differentiation. While studying formulas is not the way to learn Mathematics, this is just a quick revision before your exams. Being a math educator for over two decades , I am putting up this video to help you as I know how important it is for you to know your formulas in Mathematics. I have started with basic differentiation formulas, then proceeded to trigonometric differentiation. The chain rule for differentiation composite functions is explained. Then various methods for implicit differentiation and logarithmic differentiation are explained. Parametric differentiation is also touched upon. The session concludes with the statements of Lagrange's Mean Value Theorem, Rolle's Theorem and its applications. A good takeaway for mathematics class 12 students.
INDETERMINATE FORMS 0/0 FORM
Learn how to apply L'Hospital's rule to differentiate limits of the form 0/0.
Here, 2 problems are discussed mainly, limits of the form infinity/infinity. The first problem deals with the numerator and denominator as trigonometric functions, both tending to infinity. The second one has the numerator as a logarithmic function and the denominator as a trig function. Trigonometric properties are used here.
USE OF DIFFERENTIATION IN APPROXIMATIONS
Here, in this video, you will learn how to calculate approximations using Differentiation. Here, we use the concept of differential to find the approximate value of a function. We can find the values easily with a calculator as well! If y = f(x), we learn the differential of y, and learn the formulae used to calculate the approximate values of y. This video is application oriented. It focuses on solving problems based on the formula. We also learn about absolute error, approximate error and %error. As a teacher, I have found students getting confused about approximate error and actual value of the function. I have explained the difference in the video. So, watch this video to understand approximations. Online classes are available with emphasis on MCQ'S and case study questions. You can choose from a specific topic or the entire syllabus. For more details, you can contact me on email@example.com.