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Introduction to Calculus
  • Level Professional
  • المدة 59 ساعات hours
  • الطبع بواسطة The University of Sydney
  • Offered by

عن

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. Students taking Introduction to Calculus will: - 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).

الوحدات

Introduction to the course

    • 1 Videos
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1 Videos

  • Welcome and introduction to Module 1

Numbers and their representations

    • 3 Videos
    • 3 Readings
    • 3 Assignment
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3 Assignment

  • Real line, decimals and significant figures
  • The Theorem of Pythagoras and properties of the square root of 2
  • Algebraic expressions, surds and approximations

3 Videos

  • Real line, decimals and significant figures
  • The Theorem of Pythagoras and properties of the square root of 2
  • Algebraic expressions, surds and approximations

3 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

Equations, inequalities and solutions sets

    • 3 Videos
    • 2 Readings
    • 2 Assignment
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2 Assignment

  • Equations and inequalities
  • Sign diagrams, solution sets and intervals

3 Videos

  • Equations and inequalities
  • Sign diagrams, solution sets and intervals (Part 1)
  • Sign diagrams, solution sets and intervals (Part 2)

2 Readings

  • Notes: Equations and inequalities
  • Notes: Sign diagrams, solution sets and intervals

The Cartesian plane and distance

    • 3 Videos
    • 3 Readings
    • 3 Assignment
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3 Assignment

  • Coordinate systems
  • Distance and absolute value
  • Lines and circles in the plane

3 Videos

  • Coordinate systems
  • Distance and absolute value
  • Lines and circles in the plane

3 Readings

  • Notes: Coordinate systems
  • Notes: Distance and absolute value
  • Notes: Lines and circles in the plane

Assessment

    • 1 Assignment
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1 Assignment

  • Module 1 quiz

Introduction

    • 1 Videos
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1 Videos

  • Introduction to Module 2

Parabolas, quadratics and the quadratic formula

    • 2 Videos
    • 2 Readings
    • 2 Assignment
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2 Assignment

  • Parabolas and quadratics
  • The quadratic formula

2 Videos

  • Parabolas and quadratics
  • The quadratic formula

2 Readings

  • Notes: Parabolas and quadratics
  • Notes: The quadratic formula

Functions, composition and inversion

    • 4 Videos
    • 4 Readings
    • 4 Assignment
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4 Assignment

  • Functions as rules, with domain, range and graph
  • Polynomial and power functions
  • Composite functions
  • Inverse functions

4 Videos

  • Functions as rules, with domain, range and graph
  • Polynomial and power functions
  • Composite functions
  • Inverse functions

4 Readings

  • Notes: Functions as rules, with domain, range and graph
  • Notes: Polynomial and power functions
  • Notes: Composite functions
  • Notes: Inverse functions

Exponential and logarithmic functions

    • 3 Videos
    • 3 Readings
    • 3 Assignment
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3 Assignment

  • The exponential function
  • The logarithmic function
  • Exponential growth and decay

3 Videos

  • The exponential function
  • The logarithmic function
  • Exponential growth and decay

3 Readings

  • Notes: The exponential function
  • Notes: The logarithmic function
  • Notes: Exponential growth and decay

Circular functions and trigonometry

    • 3 Videos
    • 3 Readings
    • 3 Assignment
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3 Assignment

  • Sine, cosine and tangent
  • The unit circle and trigonometry
  • Inverse circular functions

3 Videos

  • Sine, cosine and tangent
  • The unit circle and trigonometry
  • Inverse circular functions

3 Readings

  • Notes: Sine, cosine and tangent
  • Notes: The unit circle and trigonometry
  • Notes: Inverse circular functions

Assessment

    • 1 Assignment
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1 Assignment

  • Module 2 quiz

Introduction

    • 1 Videos
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1 Videos

  • Introduction to Module 3

Rates of change and tangent lines

    • 3 Videos
    • 3 Readings
    • 3 Assignment
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3 Assignment

  • Slopes and average rates of change
  • Displacement, velocity and acceleration
  • Tangent lines and secants

3 Videos

  • Slopes and average rates of change
  • Displacement, velocity and acceleration
  • Tangent lines and secants

3 Readings

  • Notes: Slopes and average rates of change
  • Notes: Displacement, velocity and acceleration
  • Notes: Tangent lines and secants

Limits

    • 3 Videos
    • 3 Readings
    • 3 Assignment
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3 Assignment

  • Different kinds of limits
  • Limit laws
  • Limits and continuity

3 Videos

  • Different kinds of limits
  • Limit laws
  • Limits and continuity

3 Readings

  • Notes: Different kinds of limits
  • Notes: Limit laws
  • Notes: Limits and continuity

The derivative

    • 2 Videos
    • 2 Readings
    • 2 Assignment
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2 Assignment

  • The derivative as a limit
  • Finding derivatives from first principles

2 Videos

  • The derivative as a limit
  • Finding derivatives from first principles

2 Readings

  • Notes: The derivative as a limit
  • Notes: Finding derivatives from first principles

Leibniz notation and differentials

    • 3 Videos
    • 2 Readings
    • 2 Assignment
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2 Assignment

  • Leibniz notation
  • Differentials and applications

3 Videos

  • Leibniz notation
  • Differentials and applications (Part 1)
  • Differentials and applications (Part 2)

2 Readings

  • Notes: Leibniz notation
  • Notes: Differentials and applications

Assessment

    • 1 Assignment
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1 Assignment

  • Module 3 quiz

Introduction

    • 1 Videos
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1 Videos

  • Introduction to Module 4

First derivatives and turning points

    • 3 Videos
    • 3 Readings
    • 3 Assignment
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3 Assignment

  • Increasing and decreasing functions
  • Sign diagrams
  • Maxima and minima

3 Videos

  • Increasing and decreasing functions
  • Sign diagrams
  • Maxima and minima

3 Readings

  • Notes: Increasing and decreasing functions
  • Notes: Sign diagrams
  • Notes: Maxima and minima

Second derivatives and curve sketching

    • 2 Videos
    • 2 Readings
    • 2 Assignment
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2 Assignment

  • Concavity and inflections
  • Curve sketching

2 Videos

  • Concavity and inflections
  • Curve sketching

2 Readings

  • Notes: Concavity and inflections
  • Notes: Curve sketching

The Chain Rule

    • 2 Videos
    • 2 Readings
    • 2 Assignment
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2 Assignment

  • The Chain Rule
  • Applications of the Chain Rule

2 Videos

  • The Chain Rule
  • Applications of the Chain Rule

2 Readings

  • Notes: The Chain Rule
  • Notes: Applications of the Chain Rule

The Product Rule

    • 2 Videos
    • 2 Readings
    • 2 Assignment
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2 Assignment

  • The Product Rule
  • Applications of the Product Rule

2 Videos

  • The Product Rule
  • Applications of the Product Rule

2 Readings

  • Notes: The Product Rule
  • Notes: Applications of the Product Rule

The Quotient Rule

    • 2 Videos
    • 2 Readings
    • 2 Assignment
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2 Assignment

  • The Quotient Rule
  • Application of the Quotient Rule

2 Videos

  • The Quotient Rule
  • Application of the Quotient Rule

2 Readings

  • Notes: The Quotient Rule
  • Notes: Application of the Quotient Rule

Optimisation

    • 2 Videos
    • 2 Readings
    • 2 Assignment
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2 Assignment

  • Optimisation
  • The Second Derivative Test

2 Videos

  • Optimisation
  • The Second Derivative Test

2 Readings

  • Notes: Optimisation
  • Notes: The Second Derivative Test

Assessment

    • 1 Assignment
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1 Assignment

  • Module 4 quiz

Introduction

    • 1 Videos
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1 Videos

  • Introduction to Module 5

Velocity and displacement

    • 1 Videos
    • 1 Readings
    • 1 Assignment
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1 Assignment

  • Inferring displacement from velocity

1 Videos

  • Inferring displacement from velocity

1 Readings

  • Notes: Inferring displacement from velocity

Areas under curves, Riemann sums and definite integrals

    • 2 Videos
    • 2 Readings
    • 2 Assignment
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2 Assignment

  • Areas bounded by curves
  • Riemann sums and definite integrals

2 Videos

  • Areas bounded by curves
  • Riemann sums and definite integrals

2 Readings

  • Notes: Areas bounded by curves
  • Notes: Riemann sums and definite integrals

The Fundamental Theorem of Calculus and indefinite integrals

    • 3 Videos
    • 2 Readings
    • 2 Assignment
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2 Assignment

  • The Fundamental Theorem of Calculus and indefinite integrals
  • Connection between areas and derivatives

3 Videos

  • The Fundamental Theorem of Calculus and indefinite integrals
  • Connection between areas and derivatives (Part 1)
  • Connection between areas and derivatives (Part 2)

2 Readings

  • Notes: The Fundamental Theorem of Calculus and indefinite integrals
  • Notes: Connection between areas and derivatives

Integration by substitution

    • 2 Videos
    • 1 Readings
    • 1 Assignment
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1 Assignment

  • Integration by substitution

2 Videos

  • Integration by substitution (Part 1)
  • Integration by substitution (Part 2)

1 Readings

  • Notes: Integration by substitution

Symmetry and the logistic function

    • 4 Videos
    • 2 Readings
    • 2 Assignment
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2 Assignment

  • Odd and even functions
  • The logistic function

4 Videos

  • Odd and even functions (Part 1)
  • Odd and even functions (Part 2)
  • The logistic function (Part 1)
  • The logistic function (Part 2)

2 Readings

  • Notes: Odd and even functions
  • Notes: The logistic function

Conclusion

    • 1 Videos
    • 2 Readings
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1 Videos

  • The escape velocity of a rocket

2 Readings

  • Notes: The escape velocity of a rocket
  • Formula Sheet

Assessment

    • 1 Assignment
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1 Assignment

  • Module 5 quiz
David Easdown
Instructor

David Easdown