﻿ MAT1505 Lecture Notes

# MAT1505 [Jantzen] Lecture Notes

2020 brought us into the age of Zoom delivery of classes leading to organized lecture notes that can aid student learning, freeing students from note taking and allowing them to think about what bob is explaining in the classroom. These notes are the basis of our in-person lectures.

These hand written lecture notes have been scanned to PDF using the mobile phone app Adobe Scan. Our textbook Stewart Calculus 9e section numbers name the lecture files. Supplementary details from PDF notes and Maple worksheets are found at the homework log page.

Chapter 5: Integrals

5.0 Riemann definition of a definite integral etc
5.3 Fundamental Theorem of Calculus, Review plus derivative/differential notation
5.4 Indefinite Integrals
5.5a The Substitution Rule
5.5b The Substitution Rule

Chapter 6: Applications of Integration

6.1 Areas Between Curves
6.2a Volumes
6.2b Volumes
6.4 Work (Optional)
6.5 Average Value of a Function

Chapter 7: Techniques of Integration

7.1a Integration by Parts
7.1b Integration by Parts
[7.2 Trigonometric Integrals (Optional) NO ]
[7.3 Trigonometric Substitution (Optional) NO]
[7.4 Int. of Rational Fns by Partial Frac. (Optional) NO]
7.7a Approximate Integration
7.7b Approximate Integration
7.8a Improper Integrals
7.8b Improper Integrals
7.8c Improper Integrals

Chapter 8: Further Applications of Integration

8.1a Arc Length
8.1b Arc Length
8.4a Applications to Economics and Biology [business]
8.4b Applications to Economics and Biology [heart stuff]
8.5a Probability
8.5b Probability

Chapter 11: Infinite Sequences and Series

11.1 Sequences
11.2 Series (emphasize geometric series)
11.3 The Integral Test & Estimates of Sums
11.4 The Comparison Test
11.5 Alternating Series and Absolute Convergence (Alt Series)
11.5b Alternating Series and Absolute Convergence (Abs Conv)
11.6 Ratio & Root Tests (Absolute Convergence moved to previous section in 9e)
[[11.7 Strategy for Testing Series not useful for us]]
11.8 Power Series**
11.9 Representations of Functions as Power Series**
11.10a Taylor and Maclaurin Series**
11.10b Taylor and Maclaurin Series**
11.10c Taylor and Maclaurin Series**
11.11 Application of Taylor Polynomials
** emphasize these sections
11.R. Summary

Chapter 10: Parametric Equations and Polar Coordinates

10.1 Curves Defined by Parametric Equations
10.2 Calculus with Parametric Equations: tangents
10.2b Calculus with Parametric Equations: areas and arclengths
10.3 Polar Coordinates
10.4a Areas and Lengths in Polar Coordinates
10.4b Areas and Lengths in Polar Coordinates
10.4c ArcLengths in Polar Coordinates
10.4d Polar Curve Tangents
[[10.5 Conic Sections: Ellipses]]

Chapter 9: Differential Equations (if time allows)

9.0 Fun only: DEs with Maple, Power Series Solution of Linear DEs
9.1 Modeling with Differential Equations (Optional)
9.2 Direction Fields & Euler's Method (Optional)
9.3 Separable Equations (Optional)
9.4 Models for Population Growth (Optional)