Course Summary
This course is an introduction to calculus, covering limits, derivatives, integrals, and applications. The course is designed for students who have completed high school algebra and geometry.Key Learning Points
- Gain a deep understanding of the fundamental concepts of calculus
- Learn to apply calculus to real-world problems
- Develop critical thinking and problem-solving skills
Related Topics for further study
Learning Outcomes
- Develop a strong foundation in calculus
- Learn to apply calculus to real-world problems
- Improve critical thinking and problem-solving skills
Prerequisites or good to have knowledge before taking this course
- High school algebra and geometry
- Basic understanding of mathematical concepts
Course Difficulty Level
IntermediateCourse Format
- Online self-paced course
- Video lectures
- Interactive quizzes and exercises
Similar Courses
- Single Variable Calculus
- Multivariable Calculus
- Differential Equations
Related Education Paths
Notable People in This Field
- Dr. Grant Sanderson
- Dr. James Tanton
Related Books
Description
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.
Outline
- Precalculus (Setting the scene)
- 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
- 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
- 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
- Functions (Useful and important repertoire)
- 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
- 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
- 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
- Introducing the differential calculus
- 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)
- 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
- 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
- Properties and applications of the derivative
- 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
- 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
- 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
- Introducing the integral calculus
- 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
- 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
- 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
Summary of User Reviews
Discover the fundamentals of calculus with Introduction to Calculus course on Coursera. The course has received positive reviews from students and has been rated highly for its in-depth coverage of the subject matter and engaging teaching style. Many users have praised the course for its clear explanations and helpful examples.Key Aspect Users Liked About This Course
The course is praised for its clear explanations and helpful examples.Pros from User Reviews
- In-depth coverage of calculus
- Engaging teaching style
- Clear explanations
- Helpful examples
- Well-organized course material
Cons from User Reviews
- Some users found the course too challenging
- Limited interaction with instructors
- Not enough practice problems
- Lack of feedback on assignments
- Requires prior knowledge of basic calculus concepts
David EasdownTop Instructor
4.8 Raiting
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