Comparing the Midpoint and Trapezoid Rules
Compare the errors in the Midpoint and Trapezoid Rules with n =4, 8, 16, and 32 subintervals when they are applied to the following integrals (with their exact values given).
Week 7 Abnormal Psychology Notes Symptoms of Manic Episodes Inflated self-esteem or grandiosity Decreased need for sleep More talkative than usual or pressure to keep talking Subjective experience that one’s thoughts are racing or flight of ideas Distractibility In Bipolar disorders, manic episodes tend to be shorter than depressive episodes Specifiers of Bipolar Disorders Rapidly cycling bipolar disorder o 4+ severe mood episodes in a single year o Usually an individual will experience less than one full cycle in a year Mixed State o Sxs of mania and depression that occur at the same time o Very dangerous DSM-5 Controversies Removal of bereavement exclusion for Major Depressive Disorder o Bereavement exclusion as the inability to diagnose someone with MDD who just experienced a death of a loved one New: Disruptive Mood Dysregulation Disorder o Diagnosis added to address children who may be Bipolar New: Premenstrual Dysphoric Disorder o Diagnosis for extreme PMS symptoms o Use antidepressants to treat Epidemiology Major Depression is one of the most common single psychiatric disorders worldwide o 19% lifetime pre. for U.S. adults o Higher rates in women and in low-income or oppressed populations Bipolar Disorders are less common o 4% lifetime pre. for U.S. adults o Equally common in men and women o Higher rates in low-income populations Developmental Factors Depression can occur at any age, even infancy o Sxs differ by age, median age of onset is 26 years old o In childhood, gender ratio is equal, but in adolescence, rates for girls increases Week 7 Abnormal Psychology Notes Bipolar disorders can affect all ages, but diagnosis is controversial in young children o In older adults, mania and depression often result from medical illnesses Etiology Stress factors o Depressive Disorders include stress from environment and life events Exogenous (caused by external stress) vs. Endogenous (caused by internal stress) o Bipolar Disorders cannot conclude Possible indication to stress Genetic Factors o Depressive Disorders: genetics play a predisposing role in some forms Heritability: 30-40% Twins: MZ: 46% DZ: 20% o Bipolar Disorders: strong genetic basis Heritability: 60-80% Twins: MZ: 40% DZ: 5% Biochemical Factors o Depressive Disorders have abnormal NT function of monoamines (a class of NTs that deal with mood) Permissive theory: low levels of serotonin disrupts function of other NTs that affect mood Low serotonin + low NE = Depression Low serotonin + high NE = Mania Endocrine system (hormone release): people with depression have high levels of cortisol and abnormal levels of melatonin Protein deficiencies within neurons (BDNF=Brain-derived neurotrophic factor) Exposure to stress = a decrease in BDNF which = a decrease in hippocampus size Exercise increase BDNF o Bipolar Disorders have low NT function and abnormal ion activity of neuronal membranes Ions are needed to send messages down the axon of a neuron, sometimes they fire too easily or not enough Brian Anatomy, Circuits, and Structures o Depressive Disorders Prefrontal cortex hippocampus amygdala Brodmann area 25 This circuit is filled with serotonin transporters The Brodmann area 25 is much more active in depressed people Week 7 Abnormal Psychology Notes The hippocampus stops making new cells when you’re depressed and decreases in size o Bipolar disorders vary, there are several abnormal structures, such as basal ganglia and cerebellum, but roles are unclear Immune System Factors o Depressive Disorders Immune system dysregulation is due to stress, this may be a cause OR result of depression, it is a correlational finding only Psychodynamic Factors o Depressive Disorders Difference between grief and depressions (Freud) Centrality of loss – anaclitic depression (conflicted feelings) Anger turned inward; self-punitiveness Problematic relationships Impaired attachment (childhood needs were not met) Abandonment and parental criticism Children and a parents depression Cognitive Factors o Depressive Disorders Negative thinking Maladaptive attitudes, cognitive distortions or errors in thinking Beck’s negative cognitive triangle: self, world and future Negative thoughts are automatic Learned Helplessness Lack of control over rewards/punishments lead to depression o Giving up because you feel you have no control Seligman study with the dogs in the shocking box to prove learned helplessness Attribution-Helplessness Theory: internal, global, stable attributions for negative events leads to depression Sociocultural Factors o Depressive Disorders are linked with lack of social supports and isolation Strong link between gender and depression (women are more likely to be diagnosed) Cultural background Hispanics and Blacks are 50% more likely to develop depression than white people Nonwestern countries associate depression with physical factors Western countries focus on the cognitive part Week 7 Abnormal Psychology Notes Gender and Depression Females are twice as likely to be diagnosed with depression as males “Role/Life Stress” theory: demanding but undervalued roles; expected to fulfill several roles simultaneously (career, housekeeping, childcare); lower pay and harsher evaluations for same job as men Rumination theory: socialized to internalize distress while males externalize it “Lack of Control” theory: far more likely to experience forms of victimization associated with depression (rape, spousal abuse, childhood sexual abuse) and socioeconomic disadvantage Treatment for Mood Disorders Depressive Disorders o Approximately 85% of people with unipolar depression recover, some without treatment o Big range of treatment options like many types of therapy and medication Bipolar Disorders o More than 60% of patients with mania improve with medication and monitoring o Medication is the primary treatment Lithium and psychotherapy Divided into Psychological and Biological treatments Psychological Treatments Psychodynamic Therapy o Depressive Disorders Efficacy debated Focus on loss, anger, problematic childhood experiences/relationships, repetitive life patterns Can be short or long term therapy o Bipolar Disorders Supportive: identifying emotional triggers for mood swings, supporting healthy coping Behavioral therapy o Depressive Disorders Not used by itself anymore, usually combined with cognitive therapy Reintroduce clients to pleasurable activities; reinforce non-depressive behaviors; improve social skills Behavioral activations Very simple structure, activities you have to do that you enjoy Lasting effects are unclear Cognitive therapy Week 7 Abnormal Psychology Notes o Depressive Disorders Often combined with behavioral therapy (CBT) Four phases (usually fewer than 20 sessions) Increasing activities and elevating mood Challenging automatic thoughts Identifying negative thinking and biases Changing primary attitudes Acceptance and commitment therapy Accepting negative thoughts and recognizing that, and living with them to move on o Bipolar Disorders Altering belief of self as helpless Interpersonal Psychotherapy (IPT) o Depressive Disorders Focuses on problematic relationships or coping with loss of relationships Structure of CBT but content of psychodynamic theory; recognizes key role of social stressors o Bipolar Disorders Interpersonal social rhythm therapy: routines (daily activities and mood watching) Others o Feminist therapy o Family therapy o Couples therapy o Culturally-sensitive therapy