Calculus serves as the foundation of advanced subjects in all areas of mathematics. This is the first course of Calculus. The objective of this course is to introduce students to the fundamental concepts of limit, continuity, differential, and integral calculus of functions of one variable.

What will i learn?

- Define and find the limits and contiroblems.
- Apply the concept of derivatives to solve the problems.
- Determine the slope, maxima and minima of functions.

Curriculum for this course

6 Topics

Functions

3 Sub Topics

- Basic Function
- Inverse,Exponential & Logarithmic Functions
- Trigonometric Functions and their inverses

Limits

4 Sub Topics

- Concepts of Limits
- Computing Limits
- Limit at infininity &Infinite Limits
- Continuity

Derivatives

9 Sub Topics

- 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

Application of Derivatives

8 Sub Topics

- Maxima & Minima
- Meam Value Theorem
- Graphic Functions
- Optimization Problems
- Linear Optimization and Differentials
- L'Hopital Rule
- Newton's Method
- Antiderivatives

Integration

5 Sub Topics

- Approximating Area under Curves
- Definite Integrals
- Fundamental Theorem of Calculus
- Working with Integrals
- Substituting Rules

Application of Integration

6 Sub Topics

- Velocity and Net Change
- Regions Between Curves
- Volume by Slicing and by Shelling
- Length of Curves
- Surface Area
- Physical Applications

Packages

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$ |

Requirements

- 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:
- Calculus 1, often referred to as

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Description

**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.

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About the instructor

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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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