Calculus 1 | Axiom Academy

1

Limits and Continuity

Understanding the foundation of calculus through limits

38 modules

1

Approaching a DestinationINTRO

2

Racing to ZeroINTRO

3

Telescope to InfinityINTRO

4

The Epsilon-Delta GameINTRO

5

Continuous vs Broken PathsINTRO

6

The Concept of a LimitLESSON

7

Evaluating Limits GraphicallyEXAMPLE

8

Direct Substitution MethodEXAMPLE

9

Solving Limits by FactoringEXAMPLE

10

Limit ExplorerACTIVITY

11

Limit Technique SelectorACTIVITY

12

Graphical LimitsPRACTICE

13

Advanced Algebraic LimitsPRACTICE

14

The Epsilon-Delta DefinitionLESSON

15

Epsilon-Delta ProofEXAMPLE

16

Delta CalculatorACTIVITY

17

Limit Laws in ActionLESSON

18

When Limits Fail to ExistLESSON

19

Horizontal Asymptotes and End BehaviorLESSON

20

Finding Limits at InfinityEXAMPLE

21

Asymptote HunterACTIVITY

22

End Behavior PatternsPRACTICE

23

Indeterminate Forms and Algebraic TechniquesLESSON

24

Indeterminate FormsPRACTICE

25

L'Hôpital's Rule - Evaluating Indeterminate FormsLESSON

26

Evaluating lim(x→0) sin(x)/x Using L'Hôpital's RuleEXAMPLE

27

Repeated L'Hôpital's RuleEXAMPLE

28

L'Hôpital's Rule CalculatorACTIVITY

29

The Squeeze TheoremREAL WORLD

30

Defining ContinuityLESSON

31

Defining Continuity - A Calculus FoundationLESSON

32

Testing Continuity at x = 1EXAMPLE

33

Continuity Repair WorkshopACTIVITY

34

Intermediate Value TheoremREAL WORLD

35

Continuity and IVT ApplicationsPRACTICE

36

Limits and Continuity SummarySUMMARY

37

Limits and Continuity ReferenceFORMULA SHEET

38

Limits and Continuity QuizQUIZ

2

The Derivative

Introduction to derivatives and instantaneous rate of change

29 modules

1

Speedometer MathematicsINTRO

Zooming In Until StraightINTRO

5

The Derivative MachineINTRO

6

Sharp Corners and CuspsINTRO

7

Pattern Recognition - Discovering Derivative RulesINTRO

8

Average to Instantaneous Rate of ChangeLESSON

9

Finding Instantaneous VelocityREAL WORLD

10

Average to Instantaneous RateLESSON

11

Sine Wave Rate of ChangeREAL WORLD

12

Rate of Change ApplicationsPRACTICE

13

The Derivative: Formal DefinitionLESSON

14

Basic Derivative Rules from First PrinciplesLESSON

15

When Derivatives Don't ExistLESSON

16

Continuity vs DifferentiabilityLESSON

17

Differentiability DetectiveACTIVITY

18

Differentiability AnalysisPRACTICE

19

Differentiability of |x| at x = 0EXAMPLE

20

Finding f'(x) Using the Limit DefinitionEXAMPLE

21

Finding the Tangent Line at a PointEXAMPLE

22

Finding Polynomial DerivativesEXAMPLE

23

Derivative BuilderACTIVITY

24

Secant to Tangent TransformerACTIVITY

25

Graphical Derivative SketcherACTIVITY

26

Derivative Notation and InterpretationPRACTICE

27

The Derivative SummarySUMMARY

28

Derivative Fundamentals ReferenceFORMULA SHEET

29

The Derivative - Section 2 AssessmentQUIZ

3

Rules of Differentiation

Product, quotient, chain rules and special functions

48 modules

1

Simplifying Complex ProductsINTRO

2

Composition GearsINTRO

3

The Product RuleLESSON

4

Product Rule LaboratoryACTIVITY

5

Product Rule LaboratoryACTIVITY

6

Product Rule ApplicationEXAMPLE

7

Product Rule ApplicationEXAMPLE

8

The Product Rule - Differentiating Products of FunctionsLESSON

9

The Quotient RuleLESSON

10

Product and Quotient Rule ApplicationsPRACTICE

11

Product and Quotient Rule ApplicationsPRACTICE

12

The Quotient Rule - Derivatives of FractionsLESSON

13

The Chain RuleLESSON

14

Chain Rule: Chain ReactionACTIVITY

15

Chain Rule: Chain ReactionACTIVITY

16

Chain Rule MasteryPRACTICE

17

Chain Rule MasteryPRACTICE

18

Trigonometric Chain RulesPRACTICE

19

Applying the Chain RuleEXAMPLE

20

Applying the Chain RuleEXAMPLE

21

Understanding Composite Functions & The Chain RuleLESSON

22

The General Power Rule - A Chain Rule ApplicationLESSON

23

Derivatives of Sine and CosineLESSON

24

Trig Derivative WheelACTIVITY

25

Derivatives of Sine and Cosine - A Geometric ProofLESSON

26

Derivatives of Exponentials and LogarithmsLESSON

27

Exponential & Log Derivative StudioACTIVITY

28

Exponential & Logarithmic DifferentiationPRACTICE

29

The Natural Exponential FunctionLESSON

30

Implicit DifferentiationLESSON

31

Implicit DifferentiationPRACTICE

32

Implicit Differentiation of Circle EquationEXAMPLE

33

Implicit Differentiation - Finding dy/dxLESSON

34

Logarithmic Differentiation - A Powerful TechniqueLESSON

35

Logarithmic DifferentiationPRACTICE

36

Logarithmic DifferentiationEXAMPLE

37

Finding d/dx[tan(x)]EXAMPLE

38

Differentiating y = e^(2x)·ln(x² + 1)EXAMPLE

39

Nested Function DifferentiatorACTIVITY

40

Power Tower DifferentiatorACTIVITY

41

Wave AnalyzerACTIVITY

42

Implicit Curve ExplorerACTIVITY

43

Rule Decision TreeACTIVITY

44

Derivative Rule Application TrainerACTIVITY

45

Derivative Rule MatcherPRACTICE

46

Rules of Differentiation SummarySUMMARY

47

Differentiation Rules ReferenceFORMULA SHEET

48

Rules of Differentiation QuizQUIZ

4

Applications of Derivatives

Related rates, optimization, and curve sketching

45 modules

1

Peak and Valley FinderINTRO

2

Peak and Valley FinderINTRO

3

The Expanding RippleINTRO

4

Related RatesINTRO

5

Building a Function PortraitINTRO

6

Building a Function PortraitINTRO

7

Critical Points and Local ExtremaLESSON

8

Extrema ExplorerACTIVITY

9

Extrema ClassificationPRACTICE

10

The First Derivative and Function BehaviorLESSON

11

First Derivative and Function BehaviorLESSON

12

The Second Derivative and ConcavityLESSON

13

Second Derivative and ConcavityLESSON

14

Second Derivative TestLESSON

15

The Second Derivative Test - Finding Local ExtremaLESSON

16

Complete Curve SketchEXAMPLE

17

Complete Curve SketchEXAMPLE

18

Curve Sketching StudioACTIVITY

19

Curve Sketching StudioACTIVITY

20

Function DetectiveACTIVITY

21

Curve AnalysisPRACTICE

22

Optimization StrategyLESSON

23

Optimization Strategy - A Systematic ApproachLESSON

24

Box Folding Optimization ProblemEXAMPLE

25

Optimization ExampleEXAMPLE

26

Minimizing Cost of Cylindrical CanEXAMPLE

27

Optimization WorkshopACTIVITY

28

Business Optimization SuiteACTIVITY

29

Maximum Area Fence ProblemREAL WORLD

30

Optimization ProblemsPRACTICE

31

Optimization ProblemsPRACTICE

Setting Up Related Rates ProblemsLESSON

35

Related Rates SimulatorACTIVITY

36

Ladder Sliding Down WallREAL WORLD

37

Integration

Antiderivatives, Riemann sums, definite integrals, and FTC

41 modules

1

Reversing the DerivativeINTRO

2

Area Under the CurveINTRO

3

Area Under the CurveINTRO

4

Area Growth VisualizationINTRO

5

Reversing the Chain RuleINTRO

6

Introduction to AntiderivativesLESSON

7

Antiderivative Puzzle FactoryACTIVITY

8

AntiderivativesPRACTICE

9

Finding AntiderivativesEXAMPLE

10

Finding AntiderivativesEXAMPLE

11

Riemann SumsLESSON

12

Riemann Sum CalculatorACTIVITY

13

Riemann Sum CalculatorACTIVITY

14

Calculating a Riemann SumEXAMPLE

15

Calculating a Riemann SumEXAMPLE

16

Riemann Sums - Approximating Area Under a CurveLESSON

17

The Definite Integral as AreaLESSON

18

Definite Integral PropertiesPRACTICE

19

Evaluating Definite Integrals with the FTCEXAMPLE

20

Definite Integral as AreaLESSON

21

Fundamental Theorem of Calculus Part 2LESSON

22

FTC LaboratoryACTIVITY

23

Fundamental Theorem ApplicationsPRACTICE

24

Fundamental Theorem ApplicationsPRACTICE

25

Chain Rule with FTCEXAMPLE

26

FTC Part 2 - Evaluation of IntegralsLESSON

27

U-SubstitutionLESSON

28

U-Substitution TrainerACTIVITY

29

U-SubstitutionPRACTICE

30

U-Substitution IntegrationPRACTICE

31

U-Substitution IntegrationEXAMPLE

32

U-Substitution with Limit ChangesEXAMPLE

33

U-Substitution for Definite IntegralsLESSON

34

Initial Value Problems - Finding the ConstantLESSON

35

Solving Initial Value ProblemsEXAMPLE

36

Approximation LaboratoryACTIVITY

37

Area AccumulatorACTIVITY

38

Accumulation SimulatorACTIVITY

39

Integration SummarySUMMARY

40

Integration ReferenceFORMULA SHEET

41

Integration - Unit 5 QuizQUIZ

6

Applications of Integration

Area, volume, arc length, and other applications

58 modules

1

Shaded Regions Between CurvesINTRO

Hollow CylindersINTRO

5

Cylindrical ShellsINTRO

6

Measuring Curved PathsINTRO

7

Growth and Decay PatternsINTRO

8

Area Between CurvesLESSON

9

Area Between CurvesPRACTICE

10

Area Between CurvesEXAMPLE

11

Area Between Two CurvesLESSON

12

Horizontal Integration - Integrating with Respect to yLESSON

13

The Net Change TheoremLESSON

14

Net Change ApplicationsPRACTICE

15

Net Change TheoremLESSON

16

Average Value of a FunctionLESSON

17

Average Value of sin(x)EXAMPLE

18

Average Value of a FunctionLESSON

19

Volume by Cross-Sectional AreaLESSON

20

Cross Section DesignerACTIVITY

21

Volumes by Cross SectionsPRACTICE

22

The Disk MethodLESSON

23

Disk MethodPRACTICE

24

Disk Method VariationsPRACTICE

25

Volume of Revolution - Disk MethodEXAMPLE

26

The Disk Method - Volumes of RevolutionLESSON

27

Revolution VisualizerACTIVITY

28

Volume of Revolution - Disk MethodEXAMPLE

29

Washer MethodLESSON

30

Volume Using Washer MethodEXAMPLE

31

The Washer Method - Volumes of RevolutionLESSON

Shell Method ApplicationsPRACTICE

35

Volume of Revolution - Shell MethodEXAMPLE

36

The Shell Method - Volumes of RevolutionLESSON

37

Shell Method - Volume of RevolutionEXAMPLE

38

Arc Length Formula - Visual DerivationLESSON

39

Arc LengthPRACTICE

40

Finding Arc Length of y = x^(3/2)EXAMPLE

41

Exponential Growth & DecayLESSON

42

Growth and Decay ModelerACTIVITY

43

Separation of Variables - Solving Differential EquationsLESSON

44

Total Distance vs DisplacementREAL WORLD

45

Motion from AccelerationREAL WORLD

46

Compound Growth RatesREAL WORLD

47

Volume of Pyramid with Square BaseEXAMPLE

48

Newton's Law of CoolingEXAMPLE

49

Solving Differential Equations by Separation of VariablesEXAMPLE

50

Water Flow ProblemEXAMPLE

51

Area Problem GeneratorACTIVITY

52

Volume Method ComparisonACTIVITY

53

Curve Length CalculatorACTIVITY

54

Differential Equation SolverACTIVITY

55

Separable Differential EquationsPRACTICE

56

Applications of Integration SummarySUMMARY

57

Applications of Integration ReferenceFORMULA SHEET

58

Applications of Integration QuizQUIZ

7

Course Resources

Comprehensive references and practice tests

4 modules

1

Module 127LESSON

2

Problem Solving Strategy GuideSUMMARY

3

Calculus 1 Master Reference CompendiumFORMULA SHEET

4

Comprehensive Calculus 1 Practice TestQUIZ