Calculus for Sciences I & II

Description

The Calculus for Sciences I & II Content Pack is a full Möbius course developed by the University of Waterloo and spans two semesters of calculus and covers applications in the sciences. Topics covered include: functions, limits, differentiation, integration, series and sequences, differential equations, parametric curves, vector functions, and introduces multivariate calculus. This customizable resource contains 12 units of sectioned lessons and assignments enhanced with Möbius capabilities including in-lesson questions, adaptive questions, Math Apps, interactive narratives, immediate feedback, and end-of-lesson assignments.

How does Möbius take the University of Waterloo’s content to the next level?

Lessons contain interactive elements like Interactive Narratives, HTML objects, Math Apps, or Geogebra applications to help solidify difficult STEM concepts.
Learn how Möbius’ unique STEM question types throughout this content provide the best STEM learning experience.
Work with over 50 configurable assessment properties when modifying existing or building your own assessments.

Course Structure

All content is organized into 12 units for easy navigation
Concepts are presented across 73 lessons that promote Active Learning by including illustrative visualizations, interactive elements, and example problems with immediate feedback
Different forms of assessment materials are distributed across 86 assignments to evaluate student comprehension through a variety of different question types
Pull from a vast selection of over 1980 questions that you can use to create your own lessons and assignments or supplement existing ones

12 units

73 lessons

86 assignments

1980+ questions

Unit 1: Functions

1.1 Introduction to Calculus
1.2 Functions
1.3 Combining Functions
1.4 Reversing a Function
1.5 Modeling with Functions
1.6 Exponential Functions
1.7 Logarithmic Functions
1.8 Trigonometric Functions

Unit 2: Limits

2.1 Limits
2.2 Instantaneous Velocity
2.3 Limit of a Function at a Point
2.4 Continuity

Unit 3: Differentiation

3.1 The Derivative
3.2 Differentiation Rules
3.3 The Chain Rule
3.4 Implicit Differentiation

Unit 4: Applications of Differentiation

4.1 Modeling With Derivatives
4.2 Exponential Processes
4.3 Linearization
4.4 Newton's Method
4.5 Indeterminate Forms
4.6 Extreme Values
4.7 Shapes of Graphs
4.8 Optimization

Unit 5: Introduction to Integration

5.1 Anti-derivatives
5.2 Sigma Notation
5.3 Riemann Sums
5.4 Definite Integrals
5.5 The Fundamental Theorem of Calculus
5.6 Indefinite Integrals
5.7 Integration by Substitution
5.8 Areas Between Curves

Unit 6: Integration

6.1 Review of Integration
6.2 Surface Area
6.3 Arc Length
6.4 Volumes by Shells
6.5 Areas and Volumes
6.6 Improper Integrals
6.7 Integration by Partial Fractions
6.8 Trigonometric Substitutions
6.9 Integration by Parts
6.10 Trigonometric Integrals

Unit 7: Series

7.1 Introduction to Taylor Polynomials
7.2 Sequences
7.3 Series
7.4 Working with Power Series
7.5 Integral Test
7.6 Comparison Test
7.7 Power Series and Convergence
7.8 Ratio Test
7.9 Alternating Series Test
7.10 Taylor Polynomials
7.11 Taylor Approximations in Science
7.12 Taylor Series

Unit 8: Differential Equations

8.1 Differential Equations
8.2 Linear Differential Equations
8.3 Separation of Variables
8.4 Euler's Method and Direction Fields
8.5 Linear Differential Equations: Solution Behaviour
8.6 Non-Linear Differential Equations: Solution Behaviour

Unit 9: Parametric Curves and Vector-Valued Functions

9.1 Vector-valued Functions
9.2 Arc Length and Area
9.3 Polar Coordinates
9.4 Parametric Curves

Unit 10: Vector-Valued Functions

10.1 Vector-Valued Functions
10.2 Calculus of Vector-Valued Functions
10.3 Polar Coordinates

Unit 11: Multivariable Calculus

11.1 Functions of Multiple Variables
11.2 Partial Derivatives
11.3 Applications of Partial Derivatives
11.4 Double Integrals
11.5 Double Integrals in Polar Coordinates

Bi-Weekly Assignments

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Calculus for Sciences I & II

Description

How does Möbius take the University of Waterloo’s content to the next level?

Course Structure

Unit 1: Functions

1.1 Introduction to Calculus

1.2 Functions

1.3 Combining Functions

1.4 Reversing a Function

1.5 Modeling with Functions

1.6 Exponential Functions

1.7 Logarithmic Functions

1.8 Trigonometric Functions

Unit 2: Limits

2.1 Limits

2.2 Instantaneous Velocity

2.3 Limit of a Function at a Point

2.4 Continuity

Unit 3: Differentiation

3.1 The Derivative

3.2 Differentiation Rules

3.3 The Chain Rule

3.4 Implicit Differentiation

Unit 4: Applications of Differentiation

4.1 Modeling With Derivatives

4.2 Exponential Processes

4.3 Linearization

4.4 Newton's Method

4.5 Indeterminate Forms

4.6 Extreme Values

4.7 Shapes of Graphs

4.8 Optimization

Unit 5: Introduction to Integration

5.1 Anti-derivatives

5.2 Sigma Notation

5.3 Riemann Sums

5.4 Definite Integrals

5.5 The Fundamental Theorem of Calculus

5.6 Indefinite Integrals

5.7 Integration by Substitution

5.8 Areas Between Curves

Unit 6: Integration

6.1 Review of Integration

6.2 Surface Area

6.3 Arc Length

6.4 Volumes by Shells

6.5 Areas and Volumes

6.6 Improper Integrals

6.7 Integration by Partial Fractions

6.8 Trigonometric Substitutions

6.9 Integration by Parts

6.10 Trigonometric Integrals

Unit 7: Series

7.1 Introduction to Taylor Polynomials

7.2 Sequences

7.3 Series

7.4 Working with Power Series

7.5 Integral Test

7.6 Comparison Test

7.7 Power Series and Convergence

7.8 Ratio Test

7.9 Alternating Series Test

7.10 Taylor Polynomials

7.11 Taylor Approximations in Science

7.12 Taylor Series

Unit 8: Differential Equations

8.1 Differential Equations

8.2 Linear Differential Equations

8.3 Separation of Variables

8.4 Euler's Method and Direction Fields

8.5 Linear Differential Equations: Solution Behaviour

8.6 Non-Linear Differential Equations: Solution Behaviour

Unit 9: Parametric Curves and Vector-Valued Functions

9.1 Vector-valued Functions

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