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Introduction to Calculus
Intermediate
Online
6 Weeks
Free Quick Facts
| Medium Of Instructions | Mode Of Learning | Mode Of Delivery |
|---|---|---|
| English | Self Study | Video and Text Based |
Courses and Certificate Fees
| Fees Informations | Certificate Availability | Certificate Providing Authority |
|---|---|---|
| INR 2421 | yes | Coursera |
The Syllabus
Videos
- Welcome and introduction to Module 1
- Real line, decimals and significant figures
- The Theorem of Pythagoras and properties of the square root of 2
- Algebraic expressions, surds and approximations
- Equations and inequalities
- Sign diagrams, solution sets and intervals (Part 1)
- Sign diagrams, solution sets and intervals (Part 2)
- Coordinate systems
- Distance and absolute value
- Lines and circles in the plane
Readings
- Notes: Real line, decimals and significant figures
- Notes: The Theorem of Pythagoras and properties of the square root of 2
- Notes: Algebraic expressions, surds and approximations
- Notes: Equations and inequalities
- Notes: Sign diagrams, solution sets and intervals
- Notes: Coordinate systems
- Notes: Distance and absolute value
- Notes: Lines and circles in the plane
Practice Exercises
- Real line, decimals and significant figures
- The Theorem of Pythagoras and properties of the square root of 2
- Algebraic expressions, surds and approximations
- Equations and inequalities
- Sign diagrams, solution sets and intervals
- Coordinate systems
- Distance and absolute value
- Lines and circles in the plane
- Module 1 quiz
Videos
- Introduction to Module 2
- Parabolas and quadratics
- The quadratic formula
- Functions as rules, with domain, range and graph
- Polynomial and power functions
- Composite functions
- Inverse functions
- The exponential function
- The logarithmic function
- Exponential growth and decay
- Sine, cosine and tangent
- The unit circle and trigonometry
- Inverse circular functions
Readings
- Notes: Parabolas and quadratics
- Notes: The quadratic formula
- Notes: Functions as rules, with domain, range and graph
- Notes: Polynomial and power functions
- Notes: Composite functions
- Notes: Inverse functions
- Notes: The exponential function
- Notes: The logarithmic function
- Notes: Exponential growth and decay
- Notes: Sine, cosine and tangent
- Notes: The unit circle and trigonometry
- Notes: Inverse circular functions
Practice Exercises
- Parabolas and quadratics
- The quadratic formula
- Functions as rules, with domain, range and graph
- Polynomial and power functions
- Composite functions
- Inverse functions
- The exponential function
- The logarithmic function
- Exponential growth and decay
- Sine, cosine and tangent
- The unit circle and trigonometry
- Inverse circular functions
- Module 2 quiz
Videos
- Introduction to Module 3
- Slopes and average rates of change
- Displacement, velocity and acceleration
- Tangent lines and secants
- Different kinds of limits
- Limit laws
- Limits and continuity
- The derivative as a limit
- Finding derivatives from first principles
- Leibniz notation
- Differentials and applications (Part 1)
- Differentials and applications (Part 2)
Readings
- Notes: Slopes and average rates of change
- Notes: Displacement, velocity and acceleration
- Notes: Tangent lines and secants
- Notes: Different kinds of limits
- Notes: Limit laws
- Notes: Limits and continuity
- Notes: The derivative as a limit
- Notes: Finding derivatives from first principles
- Notes: Leibniz notation
- Notes: Differentials and applications
Practice Exercises
- Slopes and average rates of change
- Displacement, velocity and acceleration
- Tangent lines and secants
- Different kinds of limits
- Limit laws
- Limits and continuity
- The derivative as a limit
- Finding derivatives from first principles
- Leibniz notation
- Differentials and applications
- Module 3 quiz
Videos
- Introduction to Module 4
- Increasing and decreasing functions
- Sign diagrams
- Maxima and minima
- Concavity and inflections
- Curve sketching
- The Chain Rule
- Applications of the Chain Rule
- The Product Rule
- Applications of the Product Rule
- The Quotient Rule
- Application of the Quotient Rule
- Optimisation
- The Second Derivative Test
Readings
- Notes: Increasing and decreasing functions
- Notes: Sign diagrams
- Notes: Maxima and minima
- Notes: Concavity and inflections
- Notes: Curve sketching
- Notes: The Chain Rule
- Notes: Applications of the Chain Rule
- Notes: The Product Rule
- Notes: Applications of the Product Rule
- Notes: The Quotient Rule
- Notes: Application of the Quotient Rule
- Notes: Optimisation
- Notes: The Second Derivative Test
Practice Exercises
- Increasing and decreasing functions
- Sign diagrams
- Maxima and minima
- Concavity and inflections
- Curve sketching
- The Chain Rule
- Applications of the Chain Rule
- The Product Rule
- Applications of the Product Rule
- The Quotient Rule
- Application of the Quotient Rule
- Optimisation
- The Second Derivative Test
- Module 4 quiz
Videos
- Introduction to Module 5
- Inferring displacement from velocity
- Areas bounded by curves
- Riemann sums and definite integrals
- The Fundamental Theorem of Calculus and indefinite integrals
- Connection between areas and derivatives (Part 1)
- Connection between areas and derivatives (Part 2)
- Integration by substitution (Part 1)
- Integration by substitution (Part 2)
- Odd and even functions (Part 1)
- Odd and even functions (Part 2)
- The logistic function (Part 1)
- The logistic function (Part 2)
- The escape velocity of a rocket
Readings
- Notes: Inferring displacement from velocity
- Notes: Areas bounded by curves
- Notes: Riemann sums and definite integrals
- Notes: The Fundamental Theorem of Calculus and indefinite integrals
- Notes: Connection between areas and derivatives
- Notes: Integration by substitution
- Notes: Odd and even functions
- Notes: The logistic function
- Notes: The escape velocity of a rocket
- Formula Sheet
Practice Exercises
- Inferring displacement from velocity
- Areas bounded by curves
- Riemann sums and definite integrals
- The Fundamental Theorem of Calculus and indefinite integrals
- Connection between areas and derivatives
- Integration by substitution
- Odd and even functions
- The logistic function
- Module 5 quiz