Lecture 2
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The document discusses methods for solving different types of first-order differential equations (DEs). It explains that separable DEs can be solved by separating the variables, while linear DEs require using an integrating factor to solve for the general solution. Non-separable DEs cannot be solved by separating variables alone. Examples are provided to demonstrate solving linear first-order DEs using an integrating factor to get the general solution and imposing initial/boundary conditions to get the particular solution.
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- The cell contains organelles that perform important functions like DNA storage in the nucleus, protein synthesis in the ribosomes, and energy production in mitochondria.
Liquid
Liquids have molecules that are close together and experience stronger attractive forces than gases, allowing them to flow freely within a container but take its shape. Viscosity, a liquid's resistance to flow, depends on molecular size and intermolecular forces, and increases for more complex, polar molecules. Surface tension results from attractive forces between liquid molecules and causes the surface to contract, while vaporization occurs when high-energy molecules overcome attractive forces and escape as a gas. Vapour pressure is affected by intermolecular forces and temperature, increasing with weaker forces and higher temperatures.
Active Transport New
Active transport requires cells to use energy in the form of ATP to move substances against their concentration gradient, such as the sodium-potassium pump transporting sodium and potassium ions across nerve cell membranes. The sodium-potassium pump uses ATP to pump 3 sodium ions out and 2 potassium ions into the cell against their gradients. Transport proteins also use active transport for molecules too large to pass through the membrane on their own, such as during endocytosis and exocytosis.
The Chemicals Of Life
The document provides an overview of basic biology concepts including:
1. Atoms and elements are the building blocks of all living things, with carbon, oxygen, hydrogen, and nitrogen being the most abundant elements in living organisms.
2. Molecules and compounds are formed through chemical bonds between atoms, including covalent, ionic, and hydrogen bonds.
3. Key biomolecules include water, carbohydrates like sugars and starches, lipids, and proteins which are made of amino acids and have unique structures and functions.
Photosynthesis
The document defines photosynthesis as the process by which plants and algae convert light energy to chemical energy to produce sugars. It occurs in chloroplasts through two stages: the light-dependent reactions where light energy is captured to produce ATP and NADPH, and the light-independent reactions where carbon dioxide is fixed into carbohydrates using the ATP and NADPH. The rate of photosynthesis is affected by light intensity, carbon dioxide concentration, and temperature, with an optimum level for each factor.
Medical Microbiology
Medical microbiology is the study of microorganisms that cause disease, such as bacteria, viruses, parasites and fungi. It examines the spread and diagnosis of infectious diseases. The goal of medical microbiology is to understand how microbes cause illness and find ways to prevent and treat infections.
Paternalism
Paternalism in medicine refers to doctors making decisions for patients that override the patients' wishes. There are two types: strong paternalism intentionally overrides patients against their will, while weak paternalism assumes patients cannot understand information or that some information would burden them.
Justifications for paternalism include the vulnerability of sick patients, medical expertise, and preserving patients' confidence in their doctors. However, most medical decisions are not urgent and patients should have time to understand their conditions and state their preferences. While doctors have expertise, personal values also influence treatment decisions. Disclosure of uncertainty need not decrease effectiveness if done to involve patients in their care.
Respiration
The document defines and explains the stages of aerobic respiration including glycolysis, the Krebs cycle, and the electron transport chain. Glycolysis breaks down glucose to produce pyruvate and ATP. The Krebs cycle further breaks down pyruvate to produce NADH, FADH2, ATP, and carbon dioxide. The electron transport chain uses NADH and FADH2 to produce ATP through oxidative phosphorylation. In total, the complete aerobic respiration of one glucose molecule produces approximately 30-32 molecules of ATP.
Preference Of Patients
Patient preferences are important for clinical, ethical, legal and psychological reasons. When patients make choices about their healthcare based on their own values and experience, and these preferences are respected by physicians, it improves health outcomes. Patients who feel they are collaborating in shared decision making have greater trust in their doctors and cooperate better. Documenting a patient's informed consent also protects physicians from claims of coercion. Overall, respecting patient autonomy and using a participatory communication style leads to better clinical care.
Enzyme And Metabolism
This document provides an overview of enzymes and metabolism. It defines enzymes as proteins that catalyze chemical reactions and discusses the lock-and-key and induced-fit models of enzyme action. It also explains factors that influence enzyme activity such as pH and temperature, and describes the roles of coenzymes and enzyme inhibitors.
Lecture 6 Cell Division [Meiosis]
Meiosis is a type of cell division that produces haploid gametes from diploid germ cells for sexual reproduction. It involves one round of DNA replication followed by two nuclear divisions. The first division, meiosis I, separates homologous chromosomes. The second division, meiosis II, separates sister chromatids. This results in four haploid daughter cells each with half the number of chromosomes as the original parent cell. Meiosis ensures genetic variation between offspring and maintains chromosome number from one generation to the next.
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Lecture 2
- 3. Linear First-Order Differential Equations A first-order differential equation is said to be linear if it can be expressed in the form : Where and are functions of x.
- 4. To solve a first-order linear equation, first rewrite it (if necessary) in the standard form above then multiply both sides by the integrating factor
- 5. The resulting equation, Is then easy to solve, not because it’s exact, but because the left-hand side collapse.
- 7. Therefore, the general equation becomes Making it susceptible to an integration, which gives the solution : Do not memorize this equation for the solution ; memorize the step needed to get there.
- 8. Exercise 1 Solve Solution: This is already in the required form
- 9. With and The integrating factor is Thus the integrating factor is . Multiplying both sides of the equation by
- 13. , gives So the particular solution is: We now use the information which means and
- 14. Exercise Solve