Studying Skipping Chapters in Stewart’s Calculus? (Pearson's Edexcel IAL Background)

[XxhaathimxX]

Hi everyone,

I’m planning to self-studying physics using Young & Freedman’s University Physics alongside Stewart’s Calculus (Early Transcendentals).

So far, I’ve completed the Edexcel IAL syllabus for:

• Pure Mathematics (P1-P4)
• Mechanics (M1-M3)
• Further Math (F1-F3)

(For reference, I’ve attached course structure of each book, listing all the content covered in the textbooks I’ve completed.)

Susan Fowler’s guide suggests learning calculus alongside YF’s mechanics chapters (1–14) and finishing Stewart by the end of electromagnetism (Ch. 21–32).

My questions:

1. Can I skip parts of Stewart?
   
   i) I’ve already learned limits from this site (and solved problems) and derivatives, integrals, and basic ODEs from the above mentioned books. Should I skip certain chapters ? If so what chapters should I skip based on the material I have learned and on what chapters should I focus on?
   
   ii) Or is it safer to review everything for gaps?
   
   
2. Pacing Stewart with YF:
   
   i) Approximately how many pages or chapters of Stewart should I aim to study per YF chapter?

ii) Is there any general guideline for how to structure this parallel study plan?

Current Plan:

• I'm planning to study YF's textbook and Stewart's simultaneously,

Concerns:

• I don’t want to waste time relearning what I already know (e.g., chain rule, etc...).
• But I also don’t want to miss foundational rigor for later physics.

Final Thought

Initially, I considered starting with Mary L. Boas’ 'Mathematical Methods in the Physical Sciences' , as it seemed to cover all the math needed for undergrad physics. After which I was going to start YF's textbook, and move on to the next textbook in the sequence provided by Susan Fowler’s guide , however I later found out that Boa's book assumed that the readers knew a fair bit of multivariable calculus, so I decided to hold off.

I'm also struggling to find a detailed structured plan similar to Susan Fowler’s guide that shows how to develop physics and math together as you progress to more advanced topics.

I do have a good roadmap for math (Thanks to Math Sorcerer's video) but I haven’t found a similar, trustworthy roadmap for combining math and physics learning effectively over the long term. (I wanted a guide similar to that of Susan Fowler’s guide).

Advice appreciated! and thanks in advance.


(Since I cannot attach more than 10 files, I'll type the rest of the course structure below here)

M2

Chapter 1: Projectiles
1.1 Horizontal Projection – Page 1
1.2 Horizontal and Vertical Components – Page 2
1.3 Projection at Any Angle – Page 8
1.4 Projectile Motion Formulae – Page 14
Chapter Review 1 – Page 19


Chapter 2: Variable Acceleration
2.1 Functions of Time – Page 25
2.2 Using Differentiation – Page 28
2.3 Using Integration – Page 33
2.4 Differentiating Vectors – Page 37
2.5 Integrating Vectors – Page 39
2.6 Constant Acceleration Formulae – Page 43
Chapter Review 2 – Page 45


Chapter 3: Centres of Mass
3.1 Centre of Mass of a Set of Particles on a Straight Line – Page 51
3.2 Centre of Mass of a Set of Particles Arranged in a Plane – Page 53
3.3 Centres of Mass of Standard Uniform Plane Laminas – Page 57
3.4 Centre of Mass of a Composite Lamina – Page 61
3.5 Centre of Mass of a Framework – Page 68
3.6 Laminas in Equilibrium – Page 72
3.7 Frameworks in Equilibrium – Page 79
3.8 Non-Uniform Composite Laminas and Frameworks – Page 83
Chapter Review 3 – Page 87


Review Exercise 1 – Page 91


Chapter 4: Work and Energy
4.1 Work Done – Page 99
4.2 Kinetic and Potential Energy – Page 103
4.3 Conservation of Mechanical Energy and Work-Energy Principle – Page 107
4.4 Power – Page 111
Chapter Review 4 – Page 116


Chapter 5: Impulses and Collisions
5.1 Momentum as a Vector – Page 122
5.2 Direct Impact and Newton's Law of Restitution – Page 125
5.3 Direct Collision with a Smooth Plane – Page 131
5.4 Loss of Kinetic Energy – Page 134
5.5 Successive Direct Impacts – Page 140
Chapter Review 5 – Page 146


Chapter 6: Statics of Rigid Bodies
6.1 Static Rigid Bodies – Page 152
Chapter Review 6 – Page 157

M3

Chapter 1: Kinematics​

1.1 Acceleration Varying with Time – Page 2
1.2 Acceleration Varying with Displacement – Page 10
Chapter Review 1 – Page 16

Chapter 2: Elastic Strings and Springs​

2.1 Hooke’s Law and Equilibrium Problems – Page 21
2.2 Hooke’s Law and Dynamics Problems – Page 28
2.3 Elastic Energy – Page 31
2.4 Problems Involving Elastic Energy – Page 33
Chapter Review 2 – Page 38

Chapter 3: Dynamics​

3.1 Motion in a Straight Line with Variable Force – Page 42
3.2 Newton’s Law of Gravitation – Page 46
3.3 Simple Harmonic Motion – Page 50
3.4 Horizontal Oscillation – Page 59
3.5 Vertical Oscillation – Page 64
Chapter Review 3 – Page 72

Chapter 4: Circular Motion​

4.1 Angular Speed – Page 86
4.2 Acceleration of an Object Moving on a Horizontal Circular Path – Page 89
4.3 Three-Dimensional Problems with Objects Moving in Horizontal Circles – Page 95
4.4 Objects Moving in Vertical Circles – Page 103
4.5 Objects Not Constrained on a Circular Path – Page 110
Chapter Review 4 – Page 115

Chapter 5: Further Centres of Mass​

5.1 Using Calculus to Find the Centre of Mass of a Lamina – Page 121
5.2 Centre of Mass of a Uniform Body – Page 130
5.3 Non-Uniform Bodies – Page 141
Chapter Review 5 – Page 144

Chapter 6: Statics of Rigid Bodies​

6.1 Rigid Bodies in Equilibrium – Page 148
6.2 Toppling and Sliding – Page 152
Chapter Review 6 – Page 159


F1

Chapter 1: Complex Numbers​

1.1 Imaginary and Complex Numbers – Page 2
1.2 Multiplying Complex Numbers – Page 5
1.3 Complex Conjugation – Page 7
1.4 Argand Diagrams – Page 9
1.5 Modulus and Argument – Page 11
1.6 Modulus-Argument Form of Complex Numbers – Page 15
1.7 Roots of Quadratic Equations – Page 16
1.8 Solving Cubic and Quartic Equations – Page 18
Chapter Review 1 – Page 22

Chapter 2: Roots of Quadratic Equations​

2.1 Roots of a Quadratic Equation – Page 29
2.2 Forming Quadratic Equations with New Roots – Page 31
Chapter Review 2 – Page 34

Chapter 3: Numerical Solutions of Equations​

3.1 Locating Roots – Page 37
3.2 Interval Bisection – Page 39
3.3 Linear Interpolation – Page 41
3.4 The Newton-Raphson Method – Page 44
Chapter Review 3 – Page 47

Chapter 4: Coordinate Systems​

4.1 Parametric Equations – Page 50
4.2 The General Equation of a Parabola – Page 53
4.3 The Equation for a Rectangular Hyperbola, the Equation of the Tangent, and the Equation of the Normal – Page 60
Chapter Review 4 – Page 68

Chapter 5: Matrices​

5.1 Introduction to Matrices – Page 77
5.2 Matrix Multiplication – Page 80
5.3 Determinants – Page 85
5.4 Inverting a 2 × 2 Matrix – Page 87
Chapter Review 5 – Page 89

Chapter 6: Transformations Using Matrices​

6.1 Linear Transformations in Two Dimensions – Page 93
6.2 Reflections and Rotations – Page 97
6.3 Enlargements and Stretches – Page 102
6.4 Successive Transformations – Page 106
6.5 The Inverse of a Linear Transformation – Page 110
Chapter Review 6 – Page 113

Chapter 7: Series​

7.1 Sums of Natural Numbers – Page 117
7.2 Sums of Squares and Cubes – Page 120
Chapter Review 7 – Page 124

Chapter 8: Proof by Induction​

8.1 Proof by Mathematical Induction – Page 128
8.2 Proving Divisibility Results – Page 132
8.3 Using Mathematical Induction to Produce a Proof for a General Term of a Recurrence Relation – Page 134
8.4 Proving Statements Involving Matrices – Page 137
Chapter Review 8 – Page 139

F2

Chapter 1: Inequalities​

1.1 Algebraic Methods – Page 2
1.2 Using Graphs to Solve Inequalities – Page 8
1.3 Modulus Inequalities – Page 10
Chapter Review 1 – Page 11

Chapter 2: Series​

2.1 The Method of Differences – Page 15
Chapter Review 2 – Page 20

Chapter 3: Complex Numbers​

3.1 Exponential Form of Complex Numbers – Page 22
3.2 Multiplying and Dividing Complex Numbers – Page 23
3.3 De Moivre’s Theorem – Page 26
3.4 Trigonometric Identities – Page 29
3.5 Nth Roots of a Complex Number – Page 32
Chapter Review 3 – Page 37

Chapter 4: Further Argand Diagrams​

4.1 Loci in an Argand Diagram – Page 47
4.2 Further Loci in an Argand Diagram – Page 55
4.3 Regions in an Argand Diagram – Page 63
4.4 Further Regions in an Argand Diagram – Page 65
4.5 Transformations of the Complex Plane – Page 70
Chapter Review 4 – Page 78

Chapter 5: First-Order Differential Equations​

5.1 Solving First-Order Differential Equations with Separable Variables – Page 90
5.2 First-Order Linear Differential Equations of the form dydx+Py=Q\frac{dy}{dx} + P y = Qdxdy+Py=Q, where P and Q are functions of x – Page 91
5.3 Reducible First-Order Differential Equations – Page 95

Chapter 6: Second-Order Differential Equations​

6.1 Second-Order Homogeneous Equations – Page 106
6.2 Second-Order Non-Homogeneous Differential Equations – Page 110
6.3 Using Boundary Conditions – Page 115
6.4 Reducible Second-Order Differential Equations – Page 118
Chapter Review 6 – Page 121

Chapter 7: Maclaurin and Taylor Series​

7.1 Higher Derivatives – Page 125
7.2 Maclaurin Series – Page 126
7.3 Series Expansions of Compound Functions – Page 128
7.4 Taylor Series – Page 132
7.5 Series Solutions of Differential Equations – Page 136
Chapter Review 7 – Page 144

Chapter 8: Polar Coordinates​

8.1 Polar Coordinates and Differential Equations – Page 150
8.2 Sketching Curves – Page 153
8.3 Area Enclosed by a Polar Curve – Page 158
8.4 Tangents to Polar Curves – Page 162
Chapter Review 8 – Page 165

F3

Chapter 1: Hyperbolic Functions​

1.1 Introduction to Hyperbolic Functions – Page 2
1.2 Sketching Graphs of Hyperbolic Functions – Page 4
1.3 Inverse Hyperbolic Functions – Page 7
1.4 Identities and Equations – Page 10
Chapter Review 1 – Page 14

Chapter 2: Further Coordinate Systems​

2.1 Ellipses – Page 18
2.2 Hyperbolas – Page 20
2.3 Eccentricity – Page 22
2.4 Tangents and Normals to an Ellipse – Page 29
2.5 Tangents and Normals to a Hyperbola – Page 29
2.6 Loci – Page 33
Chapter Review 2 – Page 38

Chapter 3: Differentiation​

3.1 Differentiating Hyperbolic Functions – Page 47
3.2 Differentiating Inverse Hyperbolic Functions – Page 49
3.3 Differentiating Inverse Trigonometric Functions – Page 50
Chapter Review 3 – Page 55

Chapter 4: Integration​

4.1 Standard Integrals – Page 54
4.2 Integration – Page 55
4.3 Trigonometric and Hyperbolic Substitutions – Page 58
4.4 Integrating Expressions – Page 61
4.5 Integrating Inverse Trigonometric and Hyperbolic Functions – Page 67
4.6 Deriving and Using Reduction Formulae – Page 71
4.7 Finding the Length of an Arc of a Curve – Page 73
4.8 Finding the Area of a Surface of Revolution – Page 79
Chapter Review 4 – Page 82

Chapter 5: Vectors​

5.1 Vector Product – Page 101
5.2 Finding Areas – Page 106
5.3 Scalar Triple Product – Page 110
5.4 Straight Lines – Page 115
5.5 Vector Planes – Page 117
5.6 Solving Geometric Problems – Page 121
Chapter Review 5 – Page 130

Chapter 6: Further Matrix Algebra​

6.1 Transposing a Matrix – Page 138
6.2 The Determinant of a 3 × 3 Matrix – Page 142
6.3 The Inverse of a 3 × 3 Matrix Where It Exists – Page 146
6.4 Using Matrices to Represent Linear Transformations in 3 Dimensions – Page 152
6.5 Using Inverse Matrices to Reverse the Effect of a Linear Transformation – Page 160
6.6 The Eigenvalues and Eigenvectors of 2 × 2 and 3 × 3 Matrices – Page 165
6.7 Reducing a Symmetric Matrix to Diagonal Form – Page 175

 

[Muu9]

If you're not sure whether you should skip a chapter or not, try some of the end of chapter problems. If you can do them fine, then skip it.

 

[XxhaathimxX]

If you're not sure whether you should skip a chapter or not, try some of the end of chapter problems. If you can do them fine, then skip it.

Thanks for replying, I'll definitely do that