University of Sydney - Introduction to Calculus
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- Public/Government Institute
Introduction to Calculus at Coursera Overview
Duration | 58 hours |
Total fee | Free |
Mode of learning | Online |
Difficulty level | Intermediate |
Official Website | Explore Free Course  |
Credential | Certificate |
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Introduction to Calculus at Coursera Highlights
- Earn a certificate upon completion
Introduction to Calculus at Coursera Course details
- Gain familiarity with key ideas of precalculus, including the manipulation of equations and elementary functions (first two weeks)
- Develop fluency with the preliminary methodology of tangents and limits, and the definition of a derivative (third week)
- Develop and practice methods of differential calculus with applications (fourth week)
- Develop and practice methods of the integral calculus (fifth week)
- The focus and themes of the Introduction to Calculus course address the most important foundations for applications of mathematics in science, engineering and commerce
- The course emphasises the key ideas and historical motivation for calculus, while at the same time striking a balance between theory and application, leading to a mastery of key threshold concepts in foundational mathematics
Introduction to Calculus at Coursera Curriculum
Precalculus (Setting the scene)
Welcome and introduction to Module
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
Functions (Useful and important repertoire)
Introduction to Module
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
Introducing the differential calculus
Introduction to Module
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)
Properties and applications of the derivative
Introduction to Module
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
Introducing the integral calculus
Introduction to Module
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
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