Lecturer: Tianyu Zhang

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**Lecture 1: Scale of Physics and Vector Space**

Abstract:

We covered the materials in the first chapter. We also introduced the concept of vector space, the operations of vectors, both the vector addition, scalar multiplication inside the vector space; as well as the operations between vector spaces, for example, the change of basis transformations. We also discussed certain features of vectors, the norm (i.e., the magnitude of a vector), and the basis. We used linear combination to introduce the basis. Out of the most interested concern is the normalized basis, and also the equivalent class (recall the definition [v] in our lecture indeed is not an equivalent class, we shall fix this in the next lecture). We introduce the algebra of vectors under the help of Abelian groups and number field.

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**Lecture 2: Motion in One, Two, and Three Dimensions**

Abstract:

In this lecture we introduced the one-dimensional motion description by vectors, in particular, by matrices. We also introduced the multi-dimensional motions. Under the help of vector space property, we could then describe the forces. We also give many examples with respect to these concepts.

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In-Lecture Notes

**Lecture 3: Fundamental Results in One, Two, and Three Dimensions**

Abstract:

We proved some important results in one, two, and three dimensional motions. We then introduced some factorization of forces, and some fundamental results in Newton’s laws of forces.

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**Lecture 4: Application of Newton’s Laws**

Abstract:

In this lecture we covered the sixth chapter – the application of Newton’s Laws, the examples, the friction, the centripetal force, and the drag force and terminal speed. We offered some formulas for these equations and we listed many examples, where the solution involves three steps in general: (i) draw a free-body diagram, (ii) apply Newton’s Second Law of Force, and (iii) apply the Kinematic equations. We also gave some introduction to the work and some examples as well.

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**Lecture 5 and Lecture 6: Work and Kinetic Energy, Potential Energy and Conservation Law**

Abstract:

In this week’s lecture we have reviewed the calculus, in particular the Riemann integral, the Jordan measure, and the operations of differentiation and integration. We have covered chapter 7, chapter 8, and the first two sections of chapter 9. We also covered typical problems appear in the chapter 7 and chapter 8.

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**Lecture 7: Linear Momentum and Collisions**

Abstract:

In this week we focus on Linear Momentum and Collisions. We first introduce the linear momentum, then we derive impulse and collisions, where there are three different types of collisions: the inelastic, elastic, and perfectly inelastic. We also use the conservation of linear momentum to derive the center of mass, then we use thse concepts to solve the rocket propulsion problem.

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Lecture 8: Fixed-Axis Rotation

Abstract:

In this week we investigate the fixed-axis rotation. This type of angular motion is equivalent to the motion along a line. It follows that there is an analogous relationship between these two concepts, as a result, all the formulation in motion along a line has a corresponding formulation in the rotation. We construct the kinetic, the work-energy, the work, and the moment correspondence and then derive the Newton’s second law of force under the rotational consideration.

Pre-Lecture Notes

In-Lecture Notes