Apply the concept of derivatives to solve the problems.

Determine the slope, maxima and minima of functions.

Equations and inequalities: Solving linear and quadratic equations, linear inequalities. Division of polynomials,
synthetic division. Roots of a polynomial, rational roots; Viete Relations. Descartes' rule of signs. Solutions of
equations with absolute value sign. Solution of linear and non-linear inequalities with absolute value sign.

Functions and graphs: Domain and range of a function. Examples: polynomial, rational, piecewise-defined
functions, the absolute value of functions, and evaluation of such functions. Operations with functions: sum, product,
quotient, and composition.

Graphs of functions: linear, quadratic, piecewise-defined functions.
Lines and systems of equations: Equation of a straight line, slope, and intercept of a line, parallel and
perpendicular lines. Systems of linear equations, solution of a system of linear equations. Nonlinear systems: at
least one quadratic equation.

Limits and continuity: Functions, limit of a function. Graphical approach. Properties of limits. Theorems of limits.
Limits of polynomials, rational and transcendental functions. Limits at infinity, infinite limits, one-sided limits.
Continuity.

Derivatives: Definition, techniques of differentiation. Derivatives of polynomials and rational, exponential,
logarithmic, and trigonometric functions. The chain rule. Implicit differentiation. Rates of change in natural and
social sciences. Related rates. Linear approximations and differentials. Higher derivatives, Leibnitz's theorem.

Applications of derivatives: Increasing and decreasing functions. Relative extrema and optimization. First
derivative test for relative extrema. Convexity and point of inflection. The second derivative test for extrema.
Curve sketching. Mean value theorems. Indeterminate forms and L'Hopitals rule. Inverse functions and their
derivatives.

Integration: Anti derivatives and integrals. Riemann sums and the definite integral. Properties of Integral. The
fundamental theorem of calculus. The substitution rule.

Basic Function

Inverse,Exponential & Logarithmic Functions

Trigonometric Functions and their inverses

Concepts of Limits

Computing Limits

Limit at infininity &Infinite Limits

Continuity

Derivatives as a Function

Rules of Derivatives

Derivatives ofvTrigonometric Functions

Rate of changes

Chain Rules

Implicite Differentiation

Derivatives of Exponential and Logaritmic Functions

Related Rates

Derivatives of Inverse Trig. Functions

Maxima & Minima

Meam Value Theorem

Graphic Functions

Optimization Problems

Linear Optimization and Differentials

L'Hopital Rule

Newton's Method

Antiderivatives

Approximating Area under Curves

Definite Integrals

Fundamental Theorem of Calculus

Working with Integrals

Substituting Rules

Velocity and Net Change

Regions Between Curves

Volume by Slicing and by Shelling

Length of Curves

Surface Area

Physical Applications

Title

Lectures

Price

Inquiry Based Session-1 lesson

1

25$

Regular Package/ 4 lesson

4

100$

Standard Package/8 Lesson

8

180$

Premium Package/12

12

255$

Fast Track/16 Lesson

16

320$

Calculus 1 is a fundamental course in mathematics typically taken by undergraduate students, especially those pursuing degrees in science, engineering, economics, and mathematics-related fields. Here's a brief description of Calculus 1 and its importance:

Hi, I am Dr. Muhammad Usman graduated from Peking University in the field of applied and computational mathematics with distinguished student. I also completed my postdoc in field of computational mathematics. I have numerous research articles published in well-reputed international journals. Therefore, I have rich experience in research and supervise project students. As for as my teaching career is concerned, I have 14 years’ experience in teaching. I have taught various courses at A-level, O-level, graduate and postgraduate level. In the recent past years, I involve extensively in teaching online at A-level and O-level. Positive feedback of my past students always encourage me to deliver more in the better way. I look forward to working together with you as partners in your child’s educational growth and development!!

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